Quantum Action-Angle Variables for the Harmonic Oscillator.
Quantum Action-Angle Variables for the Harmonic Oscillator.
复制标题
DOI：
10.1103/physrevlett.77.5157
复制
发表时间：
1996
影响因子：
8.6
通讯作者：
Lewis;Lawrence;Harris
中科院分区：
文献类型：
--
作者：
Lewis;Lawrence;Harris
在由q的本征态和p的本征态构成的空间中，用两种方法显式构造了量子谐振子的共轭哈密顿量算符，这些算符是经典角变量除以振子频率的量子模拟。在相干态表象中对矩阵元素进行了计算。任何一种共轭算子都可以用来构造显式依赖于时间的算子不变量。它可以作为构造非线性、非自治哈密顿不变算子的新的微扰过程的起点。
Operators conjugate to the Hamiltonian are constructed explicitly for the quantum harmonic oscillator by two approaches in the space spanned by the eigenstates of q and the eigenstates of p. The operators are quantum analogs of a classical angle variable divided by the oscillator frequency. Matrix elements have been evaluated in the coherent state representation. Either conjugate operator can be used to construct an explicitly time-dependent operator invariant. It can be used as the starting point in a new perturbative procedure for constructing invariant operators for nonlinear, nonautonomous Hamiltonians.