Equations for probability density and for the phase of wave function in quantum mechanics and superconductivity

Abstract

The fourth order linear differential equation is obtained for the probability density considering the non-Hermitian Hamiltonian (the case of quasistationary states-complexity of energy). Third order nonlinear differential equation for the square of the modulus of the order parameter and for the phase is obtained by making use of Ginzburg-Landau equations. Three integrals of "motion" are found in the absence of the external magnetic field and two integrals are found in the presence of the external magnetic field. The analysis of these integrals is conducted. New analytical solutions are obtained.

Original language	English
Article number	082103
Journal	Journal of Mathematical Physics
Volume	50
Issue number	8
DOIs	https://doi.org/10.1063/1.3202416
Publication status	Published - 2009
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3202416

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title = "Equations for probability density and for the phase of wave function in quantum mechanics and superconductivity",

abstract = "The fourth order linear differential equation is obtained for the probability density considering the non-Hermitian Hamiltonian (the case of quasistationary states-complexity of energy). Third order nonlinear differential equation for the square of the modulus of the order parameter and for the phase is obtained by making use of Ginzburg-Landau equations. Three integrals of {"}motion{"} are found in the absence of the external magnetic field and two integrals are found in the presence of the external magnetic field. The analysis of these integrals is conducted. New analytical solutions are obtained.",

author = "Mkrtchyan, {A. R.} and Avakyan, {R. M.} and Hayrapetyan, {A. G.} and Khachatryan, {B. V.} and Petrosyan, {R. G.}",

year = "2009",

doi = "10.1063/1.3202416",

language = "English",

volume = "50",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics Publising LLC",

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TY - JOUR

T1 - Equations for probability density and for the phase of wave function in quantum mechanics and superconductivity

AU - Mkrtchyan, A. R.

AU - Avakyan, R. M.

AU - Hayrapetyan, A. G.

AU - Khachatryan, B. V.

AU - Petrosyan, R. G.

PY - 2009

Y1 - 2009

N2 - The fourth order linear differential equation is obtained for the probability density considering the non-Hermitian Hamiltonian (the case of quasistationary states-complexity of energy). Third order nonlinear differential equation for the square of the modulus of the order parameter and for the phase is obtained by making use of Ginzburg-Landau equations. Three integrals of "motion" are found in the absence of the external magnetic field and two integrals are found in the presence of the external magnetic field. The analysis of these integrals is conducted. New analytical solutions are obtained.

AB - The fourth order linear differential equation is obtained for the probability density considering the non-Hermitian Hamiltonian (the case of quasistationary states-complexity of energy). Third order nonlinear differential equation for the square of the modulus of the order parameter and for the phase is obtained by making use of Ginzburg-Landau equations. Three integrals of "motion" are found in the absence of the external magnetic field and two integrals are found in the presence of the external magnetic field. The analysis of these integrals is conducted. New analytical solutions are obtained.

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