若干量子幺正算符的构造及其应用

基于物理学中的一系列经典变换,利用坐标本征矢和动量本征矢的Fock表示,通过构造不对称积分引入了一系列量子力学算符,包括宇称算符、平移算符、压缩算符及经典坐标、动量变换对应的算符等.利用坐标表象及动量表象的完备性条件和正交性关系,证明了其幺正性及变换特性.作为应用,利用坐标—动量变换算符精确求解了坐标—动量耦合谐振子的动力学问题.

Some Quantum Unitary Operators and Their Application

Based on some classical transformation in physics,some quantum unitary operators were introduced by constructing asymmetric integration,which used the momentum eigenvector and coordinate eigenvector in Fock representation. These operator included parity operator,translation operator,squeezed operator,etc. Their unitarity and transformation properties were proved by means of the completeness conditions and orthogonal relation of representation. As application,the energy eigenvalue of the coordinate-quantum coupling harmonic oscillator was solved exactly.