### 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 | |

Publication status | Published - 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*50*(8), [082103]. https://doi.org/10.1063/1.3202416

**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.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 50, no. 8, 082103. https://doi.org/10.1063/1.3202416

}

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.

UR - http://www.scopus.com/inward/record.url?scp=69849109234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69849109234&partnerID=8YFLogxK

U2 - 10.1063/1.3202416

DO - 10.1063/1.3202416

M3 - Article

AN - SCOPUS:69849109234

VL - 50

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 8

M1 - 082103

ER -