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This review, of the understanding of quantum mechanics, is broad in scope, and aims to reflect enough of the literature to be representative of the current state of the subject. To enhance clarity, the main findings are presented in the form of a coherent synthesis of the reviewed sources. The review highlights core characteristics of quantum mechanics. One is statistical balance in the collective response of an ensemble of identically prepared systems, to differing measurement types. Another is that states are mathematical terms prescribing probability aspects of future events, relating to an ensemble of systems, in various situations. These characteristics then yield helpful insights on entanglement, measurement, and widely-discussed experiments and analyses. The review concludes by considering how these insights are supported, illustrated and developed by some specific approaches to understanding quantum mechanics. The review uses non-mathematical language precisely (terms defined) and rigorously (consistent meanings), and uses only such language. A theory more descriptive of independent reality than is quantum mechanics may yet be possible. One step in the pursuit of such a theory is to reach greater consensus on how to understand quantum mechanics. This review aims to contribute to achieving that greater consensus, and so to that pursuit.

The operator of time formalism is applied to radioactive decay. It appears that the proposed approach offers a better insight and understanding of the phenomena in a way that the decay exponential-law becomes the Boltzmann distribution in Gibbs treatment of canonical ensemble. The radioactive decay is seen as temporal canonical ensemble where the radioactive constant appears as the analog of the absolute temperature multiplied by Boltzmann constant. The stochastic character of decay process becomes plausible in the proposed approach and the explanation why decay is characterized by fixed quantity, and not by some parameter, is offered. [ABSTRACT FROM AUTHOR]

Based on the analysis of the maturity and finiteness of vibrational levels of bromine molecule in ground state and evaluating the effect on statistical computation, according to the elementary principles of quantum statistical theorem, using the full set of bromine molecular vibrational levels determined with algebra method, the statistical contribution for bromine systematical macroscopic thermodynamic properties is discussed. Thermodynamic state functions Helmholtz free energy, entropy and observable vibration heat capacity are calculated. The results show that the determination of full set of vibrational levels and maximum vibrational quantum number is the key in the correct statistical analysis of bromine systematical thermodynamic property. Algebra method results are clearly different from data of simple harmonic oscillator and the related algebra method results are no longer analytical but numerical and are superior to simple harmonic oscillator results. Compared with simple harmonic oscillator's heat capacities, the algebra method's heat capacities are more consistent with the experimental data in the given temperature range of 600-2100 K. [ABSTRACT FROM AUTHOR]

Following the generalized definition of exclusion statistics to infinite-dimensional Hilbert space [Murthy and Shankar, Phys. Rev. Lett.72, 3629 ( 1994 )] for a single-component anyonic system, we derive a simple relation between second mixed virial coefficient and the mutual exclusion statistics parameters using high-temperature expansion method for multicomponent anyonic system. The above result is derived without working in a specific model and is valid in any spatial dimensions. [ABSTRACT FROM AUTHOR]

We present a fully quantum mechanical treatment of collisional correlations beyond mean-field dynamics. Correlations are handled by an ensemble of mean-field states emerging from a stochastic propagation scheme. This is done by first propagating two-body correlations in time-dependent perturbation theory for a certain time span, reducing the coherently correlated state into an incoherent sum of two-particle-two-hole states, and then sampling this state into an ensemble of mean-field states according to the jump probability obtained from perturbation theory. The scheme is applied to a simple 1D test case calibrated to typical scales of molecules and clusters. Even for the small system size and low dimension, the scheme produces robust results. Occupation numbers and entropy show steady relaxation towards thermal equilibrium.