Quantum and Classical Exact Solutions of Harmonic Oscillator in a Time-Dependent Magnetic Field |
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| Authors: | LIANG Mai-Lin LIU Li-Yan |
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| Affiliation: | 1. Department of Applied Physics, School of Science, TianjinUniversity, Tianjin 300072, China;2. Liuhui Center for Applied Mathematics, Nankai University and Tianjin University, Tianjin 300071, China |
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| Abstract: | ![]()
In cylindrical coordinate, exact wave functionsof the two-dimensional time-dependent harmonic oscillator ina time-dependent magnetic field are derived by using the trialfunction method. Meanwhile, the exact classical solution as wellas the classical phase is obtained too. Through the Heisenbergcorrespondence principle, the quantum solution and the classicalsolution are connected together. |
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| Keywords: | harmonic oscillator magnetic field, exact wave function, exact classical solution , |
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