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

A. R. Mkrtchyan, R. M. Avakyan, A. G. Hayrapetyan, B. V. Khachatryan, R. G. Petrosyan

Research output: Contribution to journalArticle

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 languageEnglish
Article number082103
JournalJournal of Mathematical Physics
Volume50
Issue number8
DOIs
Publication statusPublished - 2009
Externally publishedYes

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Superconductivity
Probability Density
Wave Function
Quantum Mechanics
External Field
quantum mechanics
superconductivity
Magnetic Field
wave functions
State Complexity
Integrals of Motion
Third Order Differential Equation
Ginzburg-Landau Equation
differential equations
Linear differential equation
Order Parameter
Nonlinear Differential Equations
Fourth Order
Modulus
Analytical Solution

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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Equations for probability density and for the phase of wave function in quantum mechanics and superconductivity. / Mkrtchyan, A. R.; Avakyan, R. M.; Hayrapetyan, A. G.; Khachatryan, B. V.; Petrosyan, R. G.

In: Journal of Mathematical Physics, Vol. 50, No. 8, 082103, 2009.

Research output: Contribution to journalArticle

Mkrtchyan, A. R. ; Avakyan, R. M. ; Hayrapetyan, A. G. ; Khachatryan, B. V. ; Petrosyan, R. G. / Equations for probability density and for the phase of wave function in quantum mechanics and superconductivity. In: Journal of Mathematical Physics. 2009 ; Vol. 50, No. 8.
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