论文标题
对经典到达时间的Weyl量化的量子校正
Quantum corrections to the Weyl quantization of the classical time of arrival
论文作者
论文摘要
与该系统相结合的哈密顿量的到达（TOA）运算符是由加拉邦（Galapon）构建的，没有规范量化[J.数学。物理。 \ textbf {45}，3180（2004）]。构造的运算符表示为无限序列，但仅研究了主要术语，该术语被证明与Weyl定量的Toa-oserator相当于整个分析势。在本文中，我们通过明确解决扩展中的所有条款，全面说明上述托法经营者。我们将术语以外的术语解释为对经典到达时间的Weyl量化的量子校正。这些量子校正表示为相互作用电位的某些积分，并详细研究了它们的性质。特别是，对于线性系统，量子校正始终消失，但对于非线性系统，量子校正始终不存在。最后，我们以非谐振荡器电位为例。
A time of arrival (TOA) operator that is conjugate with the system Hamiltonian was constructed by Galapon without canonical quantization in [J. Math. Phys. \textbf{45}, 3180 (2004)]. The constructed operator was expressed as an infinite series but only the leading term was investigated which was shown to be equal to the Weyl-quantized TOA-operator for entire analytic potentials. In this paper, we give a full account of the said TOA-operator by explicitly solving all the terms in the expansion. We interpret the terms beyond the leading term as the quantum corrections to the Weyl quantization of the classical arrival time. These quantum corrections are expressed as some integrals of the interaction potential and their properties are investigated in detail. In particular, the quantum corrections always vanish for linear systems but nonvanishing for nonlinear systems. Finally, we consider the case of an anharmonic oscillator potential as an example.
