【摘要】 谐振子,变形振子,非简谐振子以及变形非简谐振子湮没算符高次幂的正交归一本征态都具有奇偶结构形式.正是由于这种结构特点决定了它们振幅的高次幂压缩性质.更多还原

【Abstract】 Coherent states and the extension to the even and odd coherent states, and further to the eigenstates of the higher power of the annihilation operator are basic and important macroscopic quantum states in quantum field theory. Recently, these investigations have been extended to the aharmonic oscillator and the quantum algebra with q -deformed or qs-deformed commutation relations. In this paper,the orthogonal eigenstates of the higher order of the annihilation operator of the q -deformed aharmonic oscillator are also derived. It is pointed out that these different macroscopic quantum states have similar squeezing properties of higher order amplitude. The reason is found that the orthogonal eigenstates of the higher order of the annihilation operator of the harmonic oscillator, the q -deformed oscillator, the qs -deformed oscillator, the Enharmonic oscillator and the q -deformed anharmonic oscillator all have even and odd structure, which is similar to the simple even and odd coherent states. For other systems like the system with SU(1 ,1) Lie algebra or q -deformed quantum algebra also have such properties.更多还原