Quantum three body problems using harmonic oscillator bases with different sizes

TL;DR

This paper introduces a novel method for solving the quantum three-body problem using harmonic oscillator bases of varying sizes, improving convergence and computational efficiency without approximations.

Contribution

It presents a new approach expanding wave functions on harmonic oscillator bases with different sizes, enhancing convergence and reducing computational time in quantum three-body problems.

Findings

Improved convergence over traditional methods

Exact calculation of Hamiltonian matrix elements

Reduced computational time with numerical tricks

Abstract

We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be calculated without any approximation and the precision is restricted only by the dimension of the basis. This method can be applied whatever the system under consideration. In some cases, the convergence property is greatly improved in this new scheme as compared to the old traditional method. Some numerical tricks to reduce computer time are also presented.