Improvement of the envelope theory with the dominantly orbital state method

Abstract

The envelope theory, also known as the auxiliary field method, is a simple technique to compute approximate solutions of Hamiltonians for $N$ identical particles in $D$ dimensions. The quality of the approximate eigenvalues can be improved by adding a free parameter in the characteristic global quantum number of the solutions. A method is proposed to determine the value of this parameter by comparing the eigenvalues computed with the envelope theory to the corresponding ones computed with a $N$-body generalization of the dominantly orbital state method. The accuracy of the procedure is tested with several systems.

arXiv admin note: text overlap with arXiv:1501.01383

References in corpus (3)

• Bohr-Sommerfeld quantization and meson spectroscopy
• Numerical tests of the envelope theory for few-boson systems
• Duality relations in the auxiliary field method

Cited by in corpus (12)

• Many-body forces with the envelope theory
• Tests of the Envelope Theory in One Dimension
• Quantum support to BoHua Sun's conjecture
• Envelope Theory for Systems with Different Particles
• Quasi Kepler's third law for quantum many-body systems
• Bound cyclic systems with the envelope theory
• Improvement of the Envelope Theory for Systems with Different Particles
• The envelope theory as a pedagogical tool
• Compact equations for the envelope theory
• Tests of the envelope theory for three-body forces
• Accuracy Tests of the Envelope Theory
• Upper bounds for critical coupling constants for binding some quantum many-body systems