Compact equations for the envelope theory

Abstract

The envelope theory is a method to easily obtain approximate, but reliable, solutions for some quantum many-body problems. Quite general Hamiltonians can be considered for systems composed of an arbitrary number of different particles in $D$ dimensions. In the case of identical particles, a compact set of 3 equations can be written to find the eigensolutions. This set provides also a nice interpretation and a starting point to improve the method. It is shown here that a similar set of 7 equations can be determined for a system containing an arbitrary number of two different particles.

Improved presentation. References updated. Conclusions unchanged. To appear in Braz. J. Phys

References in corpus (6)

• Numerical tests of the envelope theory for few-boson systems
• From few to many bosons inside the unitary window: a transition between universal to non-universal behavior
• An upper bound for asymmetrical spinless Salpeter equations
• Envelope Theory for Systems with Different Particles
• Quasi Kepler's third law for quantum many-body systems
• Some specific solutions to the translation-invariant $N$-body harmonic oscillator Hamiltonian

Cited by in corpus (2)

• Improvement of the Envelope Theory for Systems with Different Particles
• The envelope theory as a pedagogical tool