Exploring the Harmonic Oscillator Wave Functions

Trajectory of the harmonic oscillator in the Schrödinger wave

A trajectory of a harmonic oscillator obeying the Schrödinger wave equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The dynamics of the ‘particle’ motion and the wave function associated with the motion are proposed. The period of a round trip on the trajectory is exactly equal ...

Occupation probability of harmonic-oscillator quanta for microscopic cluster-model wave functions.

We present a new and simple method of calculating the occupation probability of the number of total harmonic-oscillator quanta for a microscopic cluster-model wave function. Examples of applications are given to the recent calculations including α+n+n-model for 6He, α+t+n+n-model for 9Li, and α+α+n-model for 9Be as well as the classical calculations of α+p+n-model for 6Li and α + α + α-model fo...

On the Harmonic Oscillator Regularization of Partition Functions

A convenient way to calculate N -particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different connection between partition functions and thermodynamic quantities with such volume regularization. This is made explicit, and its origin explained to be due to the...

Harmonic Oscillator

A generalization of the Three-Dimensional Harmonic Oscillator Basis for Wave Functions with Non-Gaussian Asymptotic Behavior

Starting from the standard harmonic oscillator basis, we construct new sets of orthonormal wave functions with non-Gaussian asymptotic spatial dependence. These new wave functions can be used to study at numerical level two-body bound systems like mesons and baryons within quark-diquark models. Generalized hyperradial functions for three-quark models are also studied. c © Electronic Journal of ...