Harmonic Oscillator: Ladder Operators

J. D. Kelley, Jacob J. Leventhal

Charles F. Hayes

Pasquale Bosso, Saurya Das

Ducharme, Robert J.

The quantum constraint equations for a relativistic three-dimensional harmonic oscillator are shown to find concise expression in terms of Lorentz covariant ladder operators. These ladder operators consist of two conjugate 4-vectors that are each constrained to generate three linearly independent combinations of ladder operator components for raising and lowering the eigenstates of the oscillator. Correspondence to the Schrödinger equation for the harmonic oscillator in the non-relativistic limit is demonstrated.

Carl W David

The ladder operator approach to the quantum mechanics of the simple harmonic oscillator is presented.

R. Montemayor, Luis F. Urrutia

In this paper we explore a similarity transformation between the Morse oscillator and the two-dimensional harmonic oscillator. This transformation enables us to determine in a simple and straightforward way, all ladder operators for the Morse oscillator and their associated algebra, avoiding the use of the factorization method.