arXiv quant-ph/00060632000-06-14quant-ph

量子谐振子的时间算符：一个表观佯谬的解决

Time operator for the quantum harmonic oscillator: resolution of an apparent paradox

Alex Granik, H. Ralph Lewis

备注：: 6 pages (latex)

摘要：

解决了一个明显的悖论，涉及到的时间运营商已导出的量子谐振子的存在。这里有一个明显的悖论，因为尽管时间算符与哈密顿量正则共轭，但已经断言不存在与哈密顿量正则共轭的算符。为了解决这个明显的悖论，我们在相位算子是对角的表示中工作。波函数的边界条件是它们在相位变量中是周期性的，这与时间算子的（连续）本征值有关。时间算子与哈密顿算子的交换子的矩阵元除了相位变量的周期函数之外还涉及相位变量本身。当在包含相位变量本身的空间中运行时，哈密顿算子不是厄米算子。当正确地考虑这种非气密性时，在对易关系的矩阵元素的评估中，明显的悖论得到解决。

英文摘要：

An apparent paradox is resolved that concerns the existence of time operators which have been derived for the quantum harmonic oscillator. There is an apparent paradox because, although a time operator is canonically conjugate to the Hamiltonian, it has been asserted that no operator exists that is canonically conjugate to the Hamiltonian. In order to resolve the apparent paradox, we work in a representation where the phase operator is diagonal. The boundary condition on wave functions is such that they be periodic in the phase variable, which is related to the (continuous) eigenvalue of the time operator. Matrix elements of the commutator of the time operator with the Hamiltonian involve the phase variable itself in addition to periodic functions of the phase variable. The Hamiltonian is not hermitian when operating in space that includes the phase variable itself. The apparent paradox is resolved when this non-hermeticity is taken into account correctly in the evaluation of matrix elements of the commutation relation.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文