Extending the four-body problem of Wolfes to non-translationally invariant interactions

Abstract

We propose and solve exactly the Schrödinger equation of a bound quantum system consisting in four particles moving on a real line with both translationally invariant four particles interactions of Wolfes type \cite{Wolf74} and additional non translationally invariant four-body potentials. We also generalize and solve exactly this problem in any $D$-dimensional space by providing full eigensolutions and the corresponding energy spectrum. We discuss the domain of the coupling constant where the irregular solutions becomes physically acceptable

15 pages

References in corpus (4)

• Novel Quantum States of the Rational Calogero Models Without the Confining Interaction
• Electron Capture and Scaling Anomaly in Polar Molecules
• Quantization and Conformal Properties of a Generalized Calogero Model
• Trigonometric identities, angular Schrödinger equations and a new family of solvable models

Cited by in corpus (3)

• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• Solvable few-body quantum problems
• Exactly solvable $N$-body quantum systems with $N=3^k(k\ge 2)$ in the $D=1$ dimensional space