Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation
Mathematical Physics
2015-06-26 v1 math.MP
Abstract
As a continuum work of Bhaumik et al who derived the common eigenvector of the number-difference operator Q and pair-annihilation operator ab (J. Phys. A9 (1976) 1507) we search for the simultaneous eigenvector of Q and (ab-a^{+}b^{+}) by setting up a complex differential equation in the bipartite entangled state representation. The differential equation is then solved in terms of the two-variable Hermite polynomials and the formal hypergeometric functions. The work is also an addendum to Mod. Phys. Lett. A 9 (1994) 1291 by Fan and Klauder, in which the common eigenkets of Q and pair creators are discussed.
Cite
@article{arxiv.math-ph/0512021,
title = {Simultaneous eigenstates of the number-difference operator and a bilinear interaction Hamiltonian derived by solving a complex differential equation},
author = {Hong-yi Fan and Wei-bo Gao},
journal= {arXiv preprint arXiv:math-ph/0512021},
year = {2015}
}