1D Quantum Harmonic Oscillator

Ying Wang

The quantum operator methods associated with the canonical transformation are discussed around the Hamiltonian of 1D harmonic oscillator problems.The origin of energy quantum and the difference between energy quantum and phonons are also analyzed.

Ray LaPierre

Rathindra Nath Das, Sourav Dutta, Archana Maji

In this article we study the presence of chaos in supersymmetric(SUSY) quantum mechanics. For that purpose we present a form of 4-point out of time order correlator(OTOC) for SUSY quantum mechanical systems using tensor product formalism. We calculate the 4-point OTOC for SUSY 1D harmonic oscillator and find that the OTOC is exactly equal to that of 1D bosonic harmonic oscillator system. In similar manner using the eigenstate representation of supersymmetric systems we calculate the generalized higher order out of time order correlator. The higher order OTOC is a more sensitive measure of chaos than the usual 4-point correlator used in literature. Finally, we calculate the generalized 2N-point OTOC for SUSY 1D harmonic oscillator.

Ashot S. Gevorkyan, A. A. Udalov

One-dimensional problem for quantum harmonic oscillator with "regular+random" frequency subjected to the external "regular+random" force is considered. Averaged transition probabilities are found.