Models of damped oscillators in quantum mechanics

Quantum Mechanics of Damped Systems

We show that the quantization of a simple damped system leads to a self-adjoint Hamiltonian with a family of complex generalized eigenvalues. It turns out that they correspond to the poles of energy eigenvectors when continued to the complex energy plane. Therefore, the corresponding generalized eigenvectors may be interpreted as resonant states. We show that resonant states are responsible for...

Local realizations of q-Oscillators in Quantum Mechanics

Representations of the quantum q-oscillator algebra are studied with particular attention to local Hamiltonian representations of the Schrödinger type. In contrast to the standard harmonic oscillators such systems exhibit a continuous spectrum. The general scheme of realization of the q-oscillator algebra on the space of wave functions for a one-dimensional Schrödinger Hamiltonian shows the exi...

Classical models of quantum mechanics

Classical models of quantum mechanics

Classical models of quantum mechanics