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Analysis of solutions of time-dependent Schrödinger equation of a particle trapped in a spherical box. (English) Zbl 1496.81053

Summary: Three sets of exact solutions of the time-dependent Schrödinger equation of a particle that is trapped in a spherical box with a moving boundary wall have been calculated analytically. For these solutions, some physical quantities such as time-dependent average energy, average force, disequilibrium, quantum similarity measures as well as quantum similarity index have been investigated. Moreover, these solutions are compared concerning these physical quantities. The time-correlation functions among these solutions are investigated.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q41 Time-dependent Schrödinger equations and Dirac equations
52A55 Spherical and hyperbolic convexity
35R37 Moving boundary problems for PDEs
47A10 Spectrum, resolvent
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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