The shift operators

Giuseppe Mussardo

Alexei S. Zhedanov

The analogue of shift for q-Bose operators is found. In contrast with the case of ordinary Bose operators this shift is a nonlinear transformation: unitary operators of shift do not form a group. Two dual systems of q-coherent states associated with these shift operators are obtained. The matrix elements of the shift operator in canonical basis are expressed via the Charlier q-polynomials.

R. Sh. Kalmetev, Yu. N. Orlov, Vsevolod Zhanovich Sakbaev

Abstract We study the Chernoff averages for random generalized shift operators in the case of noncanonical commutation relations between creation and annihilation operators. We introduce the concepts of shift-dual ladder operators and generalized shift operators. As an example, we consider a one-parameter family of commutation relations for which generalized shift operators are unitary and satisfy the semigroup property on straight lines passing through the origin. For this family, we prove that the sequence of expectations of Feynman–Chernoff iterations of random shift operators converges to a limit strongly continuous semigroup.

Cecilia Flori

AUGUST STERN

Shuai Wang, Jiang Ji-Jian, Shimin Xu +1 more

Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the multimode coordinate–momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the multimode phase shifting operator.