scholarly journals CRYPTO-HERMITIAN APPROACH TO THE KLEIN–GORDON EQUATION

2017 ◽  
Vol 57 (6) ◽  
pp. 462 ◽  
Author(s):  
Iveta Semoradova
Keyword(s):  
Quantum Mechanics ◽  
Gordon Equation ◽  
Inner Product ◽  
Indefinite Inner Product ◽  
Probability Interpretation ◽  
Klein Gordon ◽  
Common Problems ◽  
Klein Gordon Equation

We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed.

scholarly journals QUANTUM GEOMETRODYNAMICS OF THE BIANCHI-IX MODEL IN EXTENDED PHASE SPACE

1999 ◽  
Vol 14 (28) ◽  
pp. 4473-4490 ◽  
Author(s):  
V. A. SAVCHENKO ◽  
T. P. SHESTAKOVA ◽  
G. M. VERESHKOV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Invariant Solution ◽  
Closed Universe ◽  
Extended Phase ◽  
Probability Interpretation ◽  
Bianchi Ix ◽  
The Universe ◽  
Quantum Geometrodynamics ◽  
Standard Probability

A way of constructing mathematically correct quantum geometrodynamics of a closed universe is presented. The resulting theory appears to be gauge-noninvariant and thus consistent with the observation conditions of a closed universe, by that being considerably distinguished from the traditional Wheeler–DeWitt one. For the Bianchi-IX cosmological model it is shown that a normalizable wave function of the universe depends on time, allows the standard probability interpretation and satisfies a gauge-noninvariant dynamical Schrödinger equation. The Wheeler–DeWitt quantum geometrodynamics is represented a singular, BRST-invariant solution to the Schrödinger equation having no property of normalizability.

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