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 |
Fingerprint
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
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 journal › Article
}
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
VL - 50
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 8
M1 - 082103
ER -