NONAUTONOMOUS HAMILTONIAN QUANTUM SYSTEMS, OPERATOR EQUATIONS, AND REPRESENTATIONS OF THE BENDER-DUNNE WEYL-ORDERED BASIS UNDER TIME-DEPENDENT CANONICAL TRANSFORMATIONS

作者：Gianfreda M^*; Landolfi G

来源：Theoretical and Mathematical Physics, 2017, 193(1): 1444-1463.

DOI：10.1134/S004057791710004X

• Weyl ordering
• Bender-Dunne operator basis
• operator equation
• time-dependent quantum system
• quantum canonical transformation

We solve the problem of integrating operator equations for the dynamics of nonautonomous quantum systems by using time-dependent canonical transformations. The studied operator equations essentially reproduce the classical integrability conditions at the quantum level in the basic cases of one-dimensional nonautonomous dynamical systems. We seek solutions in the form of operator series in the Bender-Dunne basis of pseudodifferential operators. Together with this problem, we consider quantum canonical transformations. The minimal solution of the operator equation in the representation of the basis at a fixed time corresponds to the lowest-order contribution of the solution obtained as a result of applying a canonical linear transformation to the basis elements.

• 出版日期2017-10