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Wave-packet trains of a time-dependent harmonic oscillator

Wenhua Hai·Shengxun Huang·Kelin Gao
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Abstract

By using a test-function method, we construct $n$ exact solutions of a quantum harmonic oscillator with a time-dependent "spring constant". Any $n$-th solution describes a wave-packet train consisting of $n+1$ packets. Its center oscillates like the classically harmonic oscillator with variable frequency, and width and highness of each packet change simultaneously. When the deformation is small, it behaves like a soliton train, and the large deformation is identified with collapse and revival of the wave-packet train.

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Wenhua Hai, Shengxun Huang, Kelin Gao. 2003-01-29. Wave-packet trains of a time-dependent harmonic oscillator. https://arxiv.org/abs/quant-ph/0301156

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