Abstract

We present and investigate a new category of quantum Lissajous states for a two-dimensional Harmonic Oscillator (2DHO) having commensurate angular frequencies. The states themselves result from the projection of ordinary coherent states (i.e. quasi-classical) onto a degenerate subspace of the 2DHO. In this way, new, highly non-classical quantum mechanically stationary states arise “organically” from the highly classical but non-stationary coherent states. The connection to Lissajous figures is evident in the result that our states so defined all have probability densities that are localized along the corresponding classical Lissajous figures. We further emphasize the important interplay between the probability current density and the emergence of quantum interference in the states we examine. In doing so, we are able to present a consistent discussion of a class of states known as vortex states.

Library of Congress Subject Headings

Lissajous' curves; Harmonic oscillators; Quantum theory; Vortex theory (Astrophysics)

Publication Date

4-26-2024

Document Type

Thesis

Student Type

Graduate

Degree Name

Physics (MS)

Department, Program, or Center

Physics and Astronomy, School of

College

College of Science

Advisor

Edwin Hach

Advisor/Committee Member

Gregory Howland

Advisor/Committee Member

George Thurston

Campus

RIT – Main Campus

Plan Codes

PHYS-MS

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