Approximate solutions for N-body Hamiltonians with identical particles in D dimensions

Abstract

A method based on the envelope theory is presented to compute approximate solutions for $N$-body Hamiltonians with identical particles in $D$ dimensions ($D\ge 2$). In some favorable cases, the approximate eigenvalues can be analytically determined and can be lower or upper bounds. An application to a $N$-body system with a minimal length is studied, and a semiclassical interpretation of the generic formula obtained for the eigenvalues is given.

Section 4 extended

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Cited by in corpus (5)

• Quantum and classical probability distributions for arbitrary Hamiltonian
• Many-quark interactions: Large-$N$ scaling and contribution to baryon masses
• Improvement of the Envelope Theory for Systems with Different Particles
• The envelope theory as a pedagogical tool
• Tests of the envelope theory for three-body forces