Harmonic-oscillator excitations of precise few-body wave functions

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...

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 ...

Harmonic Oscillator

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...

Construction of analytical many-body wave functions for correlated bosons in a harmonic trap.

We develop an analytical many-body wave function to accurately describe the crossover of a one-dimensional bosonic system from weak to strong interactions in a harmonic trap. The explicit wave function, which is based on the exact two-body states, consists of symmetric multiple products of the corresponding parabolic cylinder functions and respects the analytically known limits of zero and infi...