傅里叶变换的q-振子和q-模拟中观测量的谱
Spectra of observables in the q-oscillator and q-analogue of the Fourier transform
摘要：
研究了q>1时Biedenharn-Macfarlane q振子（主要关系式为aa^+-qa^+a=1）的位置和动量算符的谱.这些算子是对称的，但不是自伴的。它们有一个单参数的自伴扩张族。这些扩展是显式导出的。给出了它们的谱和本征函数。不同扩展的谱不相交。结果表明，q振子的产生算符a^+和湮灭算符a（q>1）在没有更精确定义的情况下不能确定一个物理系统。为了确定一个物理系统，我们必须选择适当的位置和动量算子的自伴扩张。
英文摘要：
Spectra of the position and momentum operators of the Biedenharn-Macfarlane q-oscillator (with the main relation aa^+-qa^+a=1) are studied when q>1. These operators are symmetric but not self-adjoint. They have a one-parameter family of self-adjoint extensions. These extensions are derived explicitly. Their spectra and eigenfunctions are given. Spectra of different extensions do not intersect. The results show that the creation and annihilation operators a^+ and a of the q-oscillator for q>1 cannot determine a physical system without further more precise definition. In order to determine a physical system we have to choose appropriate self-adjoint extensions of the position and momentum operators.
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。
