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Quasi-Hermitian Formulation of Quantum Mechanics Using Two Conjugate Schrödinger Equations.
- Source :
-
Axioms (2075-1680) . Jul2023, Vol. 12 Issue 7, p644. 19p. - Publication Year :
- 2023
-
Abstract
- 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]
Details
- Language :
- English
- ISSN :
- 20751680
- Volume :
- 12
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Axioms (2075-1680)
- Publication Type :
- Academic Journal
- Accession number :
- 168599567
- Full Text :
- https://doi.org/10.3390/axioms12070644