Low Temperature Physics: 36, 100 (2010); https://doi.org/10.1063/1.3294430 (5 pages)
Application of the experience of numerical simulation of the mixed state of superconductors to a study of non-stationary Schrödinger equation.
A.A. Galkin Donetsk Physico-Technical Institute NANU, 72 R. Luxembourg Str., Donetsk 83114, Ukraine
Received March 17, 2009, revised June 23, 2009
The previous experience of numerical simulation of superconducting systems is applied to study the behavior of nonstationary wave function far from the equilibrium. It is shown that the normalization of the wave function plays a role of effective nonlocal interaction which leads to a localization of the function in one of the potential valleys even at infinitesimally small difference between deepness of the valleys. This principally differs from the solution of Focker–Plank equation which exponentially depends on energy and which is practically symmetric for the valleys close in deepness. At a fluctuation change of the deepness relation into the inverse one the maximum of the wave function «tunnels» from the initial valley into another one. The transition from the excited state a lower one is also studied. It is shown that the transition is accompanied by the emission of a fragment of electromagnetic wave which can be associated with a «photon».
PACS: 03.65.–w Quantum mechanics;
Key words: Ginzburg-Landau equations, Schrödinger equation, non-stationary.