The Quantization process for the Driven Quantum Well - Perturbative Expansion and the Classical Limit

Eli Eisenberg; Nadav Shnerb; Rachel Avigur

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The Quantization process for the Driven Quantum Well - Perturbative Expansion and the Classical Limit

Eli Eisenberg·Nadav Shnerb·Rachel Avigur

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Abstract

We consider the quantum mechanical behavior of a driven particle in an infinite 1D potential well. We show that the time dependent perturbation series is induced by the delicate non-trivial properties of the momentum operator in this case, namely, its non-self-adjointness. Using this expansion, we calculate the first order contribution to the cross section and the energy gain, and discuss their classical limit. In this limit the one-period energy gain converges to its classical analog - the classical local (momentum space) diffusion coefficient. Both the classical and quantum mechanical results are compared with numerical simulations.

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Eli Eisenberg, Nadav Shnerb, Rachel Avigur. 1995-12-01. The Quantization process for the Driven Quantum Well - Perturbative Expansion and the Classical Limit. https://arxiv.org/abs/cond-mat/9512003

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