Generalization of the Darboux transformation and generalized harmonic oscillators

Abstract

The Darbroux transformation is generalized for time-dependent Hamiltonian systems which include a term linear in momentum and a time-dependent mass. The formalism for the $N$-fold application of the transformation is also established, and these formalisms are applied for a general quadratic system (a generalized harmonic oscillator) and a quadratic system with an inverse-square interaction up to N=2. Among the new features found, it is shown, for the general quadratic system, that the shape of potential difference between the original system and the transformed system could oscillate according to a classical solution, which is related to the existence of coherent states in the system.

References in corpus (8)

• Supersymmetry and Quantum Mechanics
• New hydrogen-like potentials
• Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential
• Exact quantum states of a general time-dependent quadratic system from classical action
• Geometric Phase, Hannay's Angle, and an Exact Action Variable
• Unitary relations in time-dependent harmonic oscillators
• Exact coherent states in one-dimensional quantum many-body systems with inverse-square interactions
• Supersymmetry of the Nonstationary Schrödinger equation and Time-Dependent Exactly Solvable Quantum Models

Cited by in corpus (1)

• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems