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We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian. [ABSTRACT FROM AUTHOR]

We consider the Dirac quantization in the first-class formalism to investigate the hypersphere soliton model (HSM) defined on the S 3 hypersphere. To do this, we construct the first-class Hamiltonian possessing the Weyl ordering correction. In the HSM, we evaluate the baryon physical quantities such as the baryon masses, magnetic moments, axial coupling constant and charge radii, most predicted values of which are in good agreement with the corresponding experimental data. Moreover, shuffling the baryon and transition magnetic moments, we find the model independent sum rules. In the HSM we also evaluate the baryon intrinsic frequencies such as ω N = 0.87 × 10 23 s − 1 and ω Δ = 1.74 × 10 23 s − 1 of the nucleon and delta baryon, respectively, to yield the identity ω Δ = 2 ω N . Next, making use of the Nambu-Goto string action and its extended rotating bosonic string theory, we formulate the stringy photon model to obtain the energy of the string configuration, which consists of the rotational and vibrational energies of the open string. Exploiting this total string energy, we evaluate the photon intrinsic frequency ω γ = 9.00 × 10 23 s − 1 , which is comparable to the corresponding baryon intrinsic frequencies. We also predict the photon size 〈 r 2 〉 1 / 2 (photon) = 0.17 fm , which is approximately 21% of the proton magnetic charge radius. [ABSTRACT FROM AUTHOR]

We develop the theory of transformation of intensive initial nonlinear wave pulses to trains of solitons emerging at asymptotically large time of evolution. Our approach is based on the theory of dispersive shock waves in which the number of nonlinear oscillations in the shock becomes the number of solitons at the asymptotic state. We show that this number of oscillations, which is proportional to the classical action of particles associated with the small-amplitude edges of shocks, is preserved by the dispersionless flow. Then, the Poincaré–Cartan integral invariant is also constant, and therefore, it reduces to the quantization rule similar to the Bohr–Sommerfeld quantization rule for a linear spectral problem associated with completely integrable equations. This rule yields a set of "eigenvalues," which are related to the asymptotic solitons' velocities and their characteristics. It is implied that the soliton equations under consideration give modulationally stable solutions; therefore, these "eigenvalues" are real. Our analytical results agree very well with the results of numerical solutions of the generalized defocusing nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R (t) ) representing another observable. In the language of physics, the information carried by R (t) ≠ R † (t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ (t) . From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ (t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the "kinematical input" operator R (t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a (t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R (t) mimicking the birth of the Universe ("Big Bang") at t = 0 . [ABSTRACT FROM AUTHOR]

Following our previous study of the Bohr–Sommerfeld (BS) quantization condition for one-dimensional case [J. C. del Valle and A. V. Turbiner, Int. J. Mod. Phys. A36, 2150221 (2021)], we extend it to d -dimensional power-like radial potentials. The BS quantization condition for S -states of the d -dimensional radial Schrödinger equation is proposed. Based on numerical results obtained for the spectra of power-like potentials, V (r) = r m with m ∈ [ − 1 , ∞) , the correctness of the proposed BS quantization condition is established for various dimensions d. It is demonstrated that by introducing the WKB correction γ into the right-hand side of the BS quantization condition leads to the so-called exact WKB quantization condition, which reproduces the exact energies, while γ remains always very small. For m = 2 (any integer d) and for m = − 1 (at d = 2) the WKB correction γ = 0 : for S states the BS spectra coincides with the exact ones. Concrete calculations for physically important cases of linear, cubic, quartic and sextic oscillators, as well as Coulomb and logarithmic potentials in dimensions d = 2 , 3 , 6 are presented. Radial quartic anharmonic oscillator is considered briefly. [ABSTRACT FROM AUTHOR]

The angular momentum of any quantum system should be unambiguously quantized. We show that such a quantization fails for a pure Dirac monopole due to a previously overlooked field angular momentum from the monopole-electric charge system coming from the magnetic field of the Dirac string and the electric field of the charge. Applying the point-splitting method to the monopole-charge system yields a total angular momentum which obeys the standard angular momentum algebra, but which is gauge variant. In contrast it is possible to properly quantize the angular momentum of a topological 't Hooft–Polyakov monopole plus charge. This implies that pure Dirac monopoles are not viable – only 't Hooft–Polyakov monopoles are theoretically consistent with angular momentum quantization and gauge invariance. [ABSTRACT FROM AUTHOR]

Using the thin-layer quantization, we formulate the problem of a Schrödinger particle constrained to move along a coordinate surface of the bi-spherical coordinate system. In three-dimensional space, the free Schrödinger equation is not separable in this coordinate system. However, when we consider the equation for a particle constrained to a given surface, there are only two degrees of freedom. One has to introduce a geometrical potential to attach the particle to the surface. This well-known potential has two contributions: one from Gauss' curvature and the other from the mean curvature. The Schrödinger equation leads to a general Heun equation. We solve it exactly and present the eigenfunctions and plots of the probability densities, and, as an application of this methodology, we study the problem of an electric charge propagating along these coordinate surfaces in the presence of a uniform magnetic field. [ABSTRACT FROM AUTHOR]

We show that the strongly coupled field theory holographically dual to the Gubser-Rocha anti-de-Sitter Einstein-Maxwell-Dilaton theory describes not a single non-trivial AdS2 IR fixed point, but a one-parameter family. It is dual to a local quantum critical phase instead of a quantum critical point. This result follows from a detailed analysis of the possible quantizations of the gravitational theory that is consistent with the thermodynamics of the analytical Gubser-Rocha black hole solution. The analytic Gubser-Rocha black hole is only a 2-parameter subset of all possible solutions, and we construct other members numerically. These new numerical solutions correspond to turning on an additional scalar charge. Moreover, each solution has multiple holographic interpretations depending on the quantization chosen. In one particular quantization involving a multitrace deformation the scalar charge is a marginal operator. In other quantizations where the marginal multitrace operator is turned off, the analytic Gubser-Rocha black hole does not describe a finite temperature conformal fluid. [ABSTRACT FROM AUTHOR]

In this paper, we address the design of multi-user multiple-input single-output (MU-MISO) precoders for indoor visible light communication (VLC) systems. The goal is to minimize the transmitted optical power per light emitting diode (LED) under imperfect channel state information (CSI) at the transmitter side. Robust precoders for imperfect CSI available in the literature include noisy and outdated channel estimation cases. However, to the best of our knowledge, no work has considered adding robustness against channel quantization. In this paper, we fill this gap by addressing the case of imperfect CSI due to the quantization of VLC channels. We model the quantization errors in the CSI through polyhedric uncertainty regions. For polyhedric uncertainty regions and positive real channels, as is the case of VLC channels, we show that the robust precoder against channel quantization errors that minimizes the transmitted optical power while guaranteeing a target signal to noise plus interference ratio (SNIR) per user is the solution of a second order cone programming (SOCP) problem. Finally, we evaluate its performance under different quantization levels through numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, mode‐reconfigurable orbit angular momentum (OAM) waves is developed by mechanically rotating a 2 bit phase quantization (0°, 90°, 180°, and 270°) transmitarray (TA) with size 6.2λ0 × 6.2λ0 × 0.98λ0 (λ0 wavelength in free space). The TA consists of three‐layer metasurfaces (MSs), which are in the top, middle, and bottom layers, respectively. The TA is excited by a horn. The top layer MS converts the spherical wave from the horn into plane wave. The middle and bottom layers are same, and they together convert the plane wave into OAM wave with mode l, and then reconfigurable mode can be achieved by rotating the bottom layer MS. To the knowledge of the authors, it is the first time to design mechanical OAM mode reconfigurability by phase quantization TA. As example, two TAs are designed for reconfigurable modes at 15.5 GHz: (1) Among l = 1, 0, −1. (2) Among l = 2, 0, −2. The TAs have the following advantages: high gain (15.1–21.5 dBi), high aperture efficiency (the highest up to 29.2%), high purity (92.67%–98.93%), and small size (6.2λ0 × 6.2λ0). The measured and simulated results agree well, and validate the design method. The developed OAM mode reconfigurable TAs have potential application for future high capacity communication. [ABSTRACT FROM AUTHOR]

In this article, I discuss the criticisms raised against Thomas Kuhn's Black-Body Theory. These criticisms concern two issues: how to understand Planck's position with regards to the quantization of energy in 1901, and how to understand the book's relation to The Structure of Scientific Revolutions. Both criticisms, I argue, concern the notion of a paradigm: the first concerns how Boltzmann acted as an exemplar for Planck, and the second whether the book provides a paradigm change. I will then argue that both criticisms presume a conceptualization of paradigms that does not align well with Kuhn's conceptualization of it in both Structure and later work: they assume, more specifically, that sharing a paradigm presupposes sharing an interpretation of it, and that paradigm changes are essentially identical to gestalt switches. On the basis of this, I will then argue that the criticisms are misguided, that Kuhn's position regarding Planck's work is in fact quite close to the indetermination-view developed by some of his critics, and that the book fits Structure quite well. In conclusion, I will then reflect on how the narrative provided in Black-Body Theory connects with Kuhn's views on the relation between history and philosophy of science. [ABSTRACT FROM AUTHOR]

On the basis of revising the quantum concept and reinterpreting Bohr's hydrogen atom structure model in classical physics, this paper deduces the elliptical orbital energy level formula of electrons in hydrogen like atoms in detail. When the electron transition time is taken as unit time (1 s), the energy level formula is completely consistent with Bohr Sommerfeld's atomic structure Theory. [ABSTRACT FROM AUTHOR]

In this study, two effective approaches are combined which are implemented at the element design level and system design level to simultaneously improve the frequency bandwidth and aperture efficiency of a dual-polarized single-layer reflecting metasurface. At the element design level, a broadband behavior is realized by using the polarization conversion technique (PCT) which is a novel technique to enhance the bandwidth of the element. To this end, an anisotropic metasurface with the I-shaped metal patch is proposed for rotating the polarization of the wave emitted from a point source by 90 ∘ and making a continuous phase shift in a full range of 360 ∘ within 8-18 GHz. Therefore, a completely equiphase aperture is achieved leading to enhancing the metasurface performance such as directivity and aperture efficiency and reducing the sidelobe level compared to reflecting metasurface developed by 1-bit phase quantization technique. At the system design level, the three-frequency phase synthesis (TFPS) method, which is based on determining the best constant reference phase for the aperture, is used and the corresponding constant reference phases are optimized to minimize the phase error in the whole band. The combination of TFPS and PCT enhances the effectiveness of the TFPS method considerably. An 841 element reflecting metasurface with aperture dimensions of 290 cm × 290 cm is designed, simulated, and fabricated in Ku-band to verify the concept. The measurement results show that the 1-dB gain bandwidth before and after combining PCT and TFPS techniques are 17.47% (14.1–16.8 GHz) and 30.3% (14–19 GHz), respectively. In addition, the maximum aperture efficiency of the proposed metasurface is 63.62% which occurs at 14.5 GHz. [ABSTRACT FROM AUTHOR]

An approach of the proper quantization rule to find exact solution of radial Schrödinger equation for non-polynomial potentials, which are quasi exactly solvable, is developed in this work. Using this rule, the determination of the energy spectrum En for non-pollynomialy potentials is somewhat impossible and limited, which provides their energy at ground state only. To overcome this difficulty, we devised in this approach the potential into two potentials: an exact potential Ve(r) and a non-linear extension Va(r), the potential will be expressed as:V (r) = Ve(r)+Va(r), then calculate the energy level εn and the ground state ε0 energy for exactly solvable potential Ve(r) using the proper quantization rule, from which an analytical expression of energie En for non-polynomial potential V (r) related with the ground level energy E0 is found easily. We conclude that the study of non-exactly potential remain to the study of the first exactly solvable potential. [ABSTRACT FROM AUTHOR]

Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly supported, it is smaller than any of its dual quantizations while the dominated original measure is greater than any of its stationary (and therefore any of its quadratic optimal) primal quantization. Moreover, the quantization errors then correspond to martingale couplings between each original probability measure and its quantization. This permits to prove that any martingale coupling between the original probability measures can be approximated by a martingale coupling between their quantizations in Wassertein distance with a rate given by the quantization errors but also in the much finer adapted Wassertein distance. As a consequence, while the stability of (Weak) Martingale Optimal Transport problems with respect to the marginal distributions has only been established in dimension 1 so far, their value function computed numerically for the quantized marginals converges in any dimension to the value for the original probability measures as the numbers of quantization points go to ∞. [ABSTRACT FROM AUTHOR]

The hybrid beamforming can significantly improve the spectral and energy efficiencies of the millimeter‐wave (mmWave) massive multiple input multiple output (MIMO) systems without obvious performance loss. However, the fundamental limitation of existing hybrid beamforming is that they include high‐resolution analog‐to‐digital converters (ADCs) which consume high power. To overcome this fundamental limitation, in this paper, spectrum and energy efficient mmWave massive MIMO transmission scheme is proposed that jointly optimizes the hybrid combiner and the number of ADC bits. Particularly, the hybrid combiner is presented as a combination of three parts: the analog combiner matrix, the quantization matrix, and the digital baseband matrix which is based on the Kalman filter. Unlike most existing works that rely on sumrate optimization to design the hybrid combiner, in this work, the mean square error (MSE) is chosen as the main performance metric to describe the reliability of the system. Simulations results confirm that the proposed Kalman based hybrid combiner exhibits the best performance in terms of spectral and energy efficiencies compared to minimum mean square error (MMSE) and zero forcing (ZF) receivers. [ABSTRACT FROM AUTHOR]

Efficient quantizer design is vital in high‐speed optical receivers. In this paper, the authors propose a three‐level (1.5‐bit) reliability‐based quantizer for low‐complexity soft decoding of low‐density parity‐check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate‐compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability‐based quantizer, and it is shown that the resulting quantizer‐aware LDPC codes significantly outperform other existing codes of similar rates. [ABSTRACT FROM AUTHOR]

The system under study is the Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations t = f (t ~) ) decay probability is defined and thus "observers" which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point a = 0 (where a the radial scale factor) is calculated to be of the order ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation. [ABSTRACT FROM AUTHOR]

Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin symmetries and interactions. Several yes-go and no-go results on higher-spin diffeomorphisms are collected from the mathematical literature in order to propose a generalisation of the algebra of differential operators on which higher-spin diffeomorphisms are well-defined. This work is dedicated to the memory of Christiane Schomblond, who taught several generations of Belgian physicists the formative rigor and delicate beauty of theoretical physics. [ABSTRACT FROM AUTHOR]

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler--DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1 + 5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe--antiuniverse pairs. [ABSTRACT FROM AUTHOR]

We experimentally demonstrated 16384-ary quadrature amplitude modulation (16384QAM) mobile fronthaul based on 3-amplitude quantization high-pass Delta-sigma Modulation (DSM) in the O band intensity-modulated direct detection (IM/DD) system. By using 3-amplitude quantized high-pass DSM, we successfully quantize the analog waveform of intermediate frequency (IF) Orthogonal Frequency Division Multiplexing (OFDM) signal into 3-Level Pulse Amplitude Modulation (PAM3) signal, and 1 GHz bandwidth 16384-QAM and 1024QAM are successful transmission in 20Gb/s IM/DD link. 0.63% Error Vector Magnitude (EVM) of 16384QAM and 0.7% EVM of 2048QAM are achieved after 25km SSMF and 50km SSMF transmission, respectively. The signal-to-noise ratio (SNR) of the retrieved OFDM signal is 43 dB, which shows that the proposed scheme can support 16384QAM mobile fronthaul network. [ABSTRACT FROM AUTHOR]

In this paper we investigate the exactness of the WKB quantization condition for translationally shape invariant systems. In particular, using the formalism of supersymmetric quantum mechanics, we generalize the Langer correction and show that it generates the exact quantization condition for all conventional potentials. We also prove that this correction is related to the previously proven exactness of SWKB for these potentials. • We introduced a generalized Langer correction for all conventional potentials. • We demonstrated that this correction regularizes the wave functions near singularities. • We proved that the generalized Langer correction generates the exact quantization condition for all conventional potentials. • We demonstrated a connection between the exactness of WKB with generalized Langer corrections and SWKB. [ABSTRACT FROM AUTHOR]

A Digital-to-Time Converter based (DTC-based) fractional- N digital phase-locked loop (DPLL) using probability-density-shaping (PDS) spur immunity and quantization phase (Q-noise) reduction techniques is presented. PDS-DSM is used to generate a loop spur immunity control code for DTC. A diff type dither is proposed to further suppress the fractional spur. The loop nonlinearity will not cause fractional spurs if certain conditions are obeyed. Moreover, to reduce the quantization noise, a configurable Phase Interpolator (PI) with 0.125/0.25/0.5/1.0 division step is integrated with a multi-module divider (MMDIV), leading to an 18-dB Q-noise suppression. A reference doubler with duty-cycle correction is adopted to further reduce phase noise. The fractional spurs are greatly mitigated by combining the PDS-DSM and phase interpolator. A DPLL prototype using the aforementioned techniques was designed in a 40-nm standard CMOS process, occupying a 0.99 mm2 silicon area. At a near-integer- N frequency, i.e., near 2.23 GHz, with PDS turned on and off, the post-layout simulated fractional spur is −59 dBc and −20 dBc, respectively. The RMS jitter of the whole chip is 4.218 ps, corresponding to a figure of merit (FOM) of −220.5 dB. [ABSTRACT FROM AUTHOR]

The spectrum of single-particle states of charge carriers in the β-HgS quantized layer of the β-CdS/β-HgS/β-CdS cylindrical nanoheterostructure is considered in the approximation of the isotropic effective mass. Consideration is carried out for the most interesting case, when only the first size quantization subband is filled. The cases of strong quantization of the carriers' motion in both the transverse-radial and longitudinal directions are considered separately. The splitting of the valence band into subbands of heavy and light holes is also taken into account. The dependence of the position of the chemical potential of electrons and holes on the quantization energy of charge carriers is obtained. Explicit expressions are obtained for the dependence of the density, internal energy, and heat capacity of charge carriers in the β-HgSlayer on the geometric sizes of the system and its temperature, and the corresponding graphic illustrations are presented. The influence of a longitudinal external uniform electric field on the statistical distribution of carriers in the β-HgS layer is also considered. An explicit dependence of the chemical potential and other statistical characteristics of the sample on the magnitude of the perturbing field has been obtained. [ABSTRACT FROM AUTHOR]

We are focused on the idea that observables in quantum physics are a bit more then just hermitian operators and that this is, in general, a "tricky business". The origin of this idea comes from the fact that there is a subtle difference between symmetric, hermitian, and self-adjoint operators which are of immense importance in formulating Quantum Mechanics. The theory of self-adjoint extensions is presented through several physical examples and some emphasis is given on the physical implications and applications. [ABSTRACT FROM AUTHOR]

We discuss thermofield double QFT at real time, in the large N limit. First, we establish a (dynamical) symmetry, which we argue holds in general for the real-time portion of the Schwinger–Kelydish contour. At large N, this symmetry is seen to generate a one-parameter degeneracy of stationary collective solutions. The construction is explicitly worked out on an example of the O (N) vector QFT. As a nontrivial application, we describe the construction of the corresponding (large N) thermofield double state in real-time collective formalism. [ABSTRACT FROM AUTHOR]

The modified path integral representation of Wigner functions and the new Monte Carlo approach has been suggested to account for the impact of the interparticle interaction on the Pauli exclusion principle of fermions. This approach also allows to calculate the momentum distribution functions and to reduce the "sign problem" that is inaccessible to the standard path integral Monte Carlo methods. The obtained pair electron–electron distribution functions for the "uniform electron gas" demonstrate the short-range quantum ordering of electrons associated with exchange-correlation excitons. The exchange-correlation exciton is caused by the interaction of electrons with positively charged exchange holes and the excluded volume effect. The developed approach allows one to study the density–temperature range of the exciton arising, existence, and decay. Using the potential of the mean force and semiclassical Bohr–Sommerfeld quantization condition, we have demonstrated the existence of bound states disturbing the Maxwellian distribution and estimated their average energy levels. The exchange-correlation excitons have not been observed earlier in the standard path integral Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Simple Summary: We clarify the question of clock transformations and trajectories in quantum cosmology in a vacuum Bianchi I minisuperspace. We consider a simple cosmological model consisting of an empty Bianchi I Universe, whose Hamiltonian we deparametrise to provide a natural clock variable. The model thus effectively describes an isotropic universe with an induced clock given by the shear. By quantising this model, we obtain various different possible bouncing trajectories (semiquantum expectation values on coherent states or obtained by the de Broglie–Bohm formulation) and explicit their clock dependence, specifically emphasising the question of symmetry across the bounce. [ABSTRACT FROM AUTHOR]

• Present a new quantization rule to energy spectrum. • Its final form expressed by original parameters appearing in general form of SE. • An analytical formula can be found without difficulty. • A few special cases are discussed. In this paper, a new quantization rule to calculate energy spectrum is presented for the bound state problem in non-relativistic quantum mechanics based on the parametric Nikiforov-Uvarov (NU) method. Moreover, it is observed that its final form is conveniently expressed in terms of the original parameters that appear in the general form of the Schrödinger equation. As a result, an analytical formula to the bound state problem is written out explicitly in a straightforward manner without difficulty. The fool-proof nature of the method will appeal to the theorist who requires an analytical solution on the fly. A few special cases arising from this formula are also provided to demonstrate its accuracy. [ABSTRACT FROM AUTHOR]