标题： 量子化过程对于驱动量子阱 - 扰动展开和经典极限 显示英文标题

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

摘要： 我们考虑了在一维无限深势阱中受驱动粒子的量子力学行为。我们表明，时变微扰级数在这种情况下由动量算符的微妙非平凡性质所引发，即其非自伴性。利用这一展开，我们计算了截面和能量增益的一阶贡献，并讨论了它们的经典极限。在这个极限下，单周期的能量增益收敛于其经典对应物——经典局部（动量空间）扩散系数。我们将经典和量子力学的结果与数值模拟进行了比较。 显示英文摘要

摘要： 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.