Matrix Elements of Arbitrary Exponential Quadratic Operator in Multi－ Dimensional Phase Space

Abstract

Utilizing the normal and antinomal product representative of exponential quadrat ic operator in multi－dimensional phase space we give the exact expressions of matrix element for arbitrary exponential quadratic operator. Thus we derive the partition function and wave function of the system of quadratic Hamiltonian with out the knowledge of energy spectrum and eigenfunctions.

Analytic Expression of Arbitrary Matrix Elements for Boson Exponential Quadratic Polynomial Operators

“…It is easy to verify that equation ( 24) is consistent with that of Pan and co-workers and Xu and coworkers. [1,2] To sum up, the results of present paper universally apply to all cases that the exponential operators or Hamiltonians are boson quadratic polynomial forms. Using the results of present paper, one will change the calculation of operators into the algebraic calculation or Gaussian multiple integral of C number.…”

“…the calculation of the density matrix, Feynman's propagator, scattering matrix, etc. Recently, Pan and co-workers [1] and Xu and co-workers [2] have presented approaches to calculate the matrix elements of exponential quadratic operators in Fock and phase space, respectively. Motivated by Refs.…”