Research on the dynamic problems of 3D cross coupling quantum harmonic oscillator by virtue of intermediate representation vertical bar x >(lambda,nu)

摘要

The intermediate representation (namely intermediate coordinate-momentum representation) vertical bar x >(lambda,nu) are introduced and employed to research the expression of the operator tau(p) over cap + sigma(x) over cap in intermediate representation vertical bar x >(lambda,nu). The systematic Hamilton operator (H) over cap of 3D cross coupling quantum harmonic oscillator was diagonalized by virtue of quadratic form theory. The quantity of lambda, nu, tau and sigma were figured out. The dynamic problems of 3D cross coupling quantum harmonic oscillator are researched by virtue of intermediate representation. The energy eigen-value and eigenwave function of 3D cross coupling quantum harmonic oscillator were obtained in intermediate representation. The importance of intermediate representation was discussed. The results show that the Radon transformation of Wigner operator is just the projectional operator x >(lambda,nu lambda,nu)< x vertical bar(lambda,nu), and the Radon transformation of Wigner function is just a margin distribution.