Some specific solutions to the translation-invariant $N$-body harmonic oscillator Hamiltonian

Abstract

The resolution of the Schrödinger equation for the translation-invariant $N$-body harmonic oscillator Hamiltonian in $D$ dimensions with one-body and two-body interactions is performed by diagonalizing a matrix $\mathbb{J}$ of order $N-1$. It has been previously established that the diagonalization can be analytically performed in specific situations, such as for $N\le 5$ or for $N$ identical particles. We show that the matrix $\mathbb{J}$ is diagonal, and thus the problem can be analytically solved, for any number of arbitrary masses provided some specific relations exist between the coupling constants and the masses. We present analytical expressions for the energies under those constraints.

References in corpus (2)

• Numerical tests of the envelope theory for few-boson systems
• Envelope Theory for Systems with Different Particles

Cited by in corpus (2)

• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Improvement of the Envelope Theory for Systems with Different Particles