Some results on the rotated infinitely deep potential and its coherent states

Abstract

The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is because the Swanson Hamiltonian is deeply connected with that of a standard quantum Harmonic oscillator, after a suitable rotation in configuration space is performed. In this paper we consider a rotated version of a different quantum system, the infinitely deep potential, and we consider some of the consequences of this rotation. In particular, we show that differences arise with respect to the Swanson model, mainly because of the technical need of working, here, with different Hilbert spaces, rather than staying in L 2 (R). We also construct Gazeau-Klauder coherent states for the system, and analyse their properties.

Exact Solutions for Time-Dependent Non-Hermitian Oscillators: Classical and Quantum Pictures

“…Formulated to study transitions of probability amplitudes that are generated by non-unitary time evolutions, the model developed by Swanson has been revisited and studied in different branches of physics and mathematical physics [44][45][46][47][48][49][50]. Quite remarkably, the Swanson Hamiltonian can be connected with the Hamiltonian of the harmonic oscillator by the appropriate rotation in configuration space [51], which clarifies the solvability of the model.…”

Exact solutions for time-dependent non-Hermitian oscillators: classical and quantum pictures

“…Formulated to study transitions of probability amplitudes that are generated by non-unitary time evolutions, the model developed by Swanson is revisited and studied in different branches of physics and mathematical physics [44][45][46][47][48][49][50]. Quite remarkably, the Swanson Hamiltonian can be connected with the Hamiltonian of the harmonic oscillator by the appropriate rotation in configuration space [51], which clarifies the solvability of the model.…”