Eigenstates with the auxiliary field method

Abstract

The auxiliary field method is a powerful technique to obtain approximate closed-form energy formulas for eigenequations in quantum mechanics. Very good results can be obtained for Schrödinger and semirelativistic Hamiltonians with various potentials, even in the case of many-body problems. This method can also provide approximate eigenstates in terms of well known wavefunctions, for instance harmonic oscillator or hydrogen-like states, but with a characteristic size which depends on quantum numbers. In this paper, we consider two-body Schrödinger equations with linear, logarithmic and exponential potentials and show that analytical approximations of the corresponding eigenstates can be obtained with the auxiliary field method, with a very good accuracy in some cases.

Extended version published in J. Phys. A

References in corpus (8)

• Bohr-Sommerfeld quantization and meson spectroscopy
• The quantum N-body problem and the auxiliary field method
• Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation
• Some equivalences between the auxiliary field method and the envelope theory
• Semirelativistic Hamiltonians and the auxiliary field method
• Extensions of the auxiliary field method to solve Schrödinger equations
• Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials
• Accuracy of Auxiliary Field Approach for Baryons

Cited by in corpus (10)

• Numerical tests of the envelope theory for few-boson systems
• The quantum N-body problem with a minimal length
• Light baryon masses in different large-$N_c$ limits
• The auxiliary field method in quantum mechanics
• An upper bound for asymmetrical spinless Salpeter equations
• Duality relations in the auxiliary field method
• Lagrange-mesh calculations and Fourier transform
• Further developments for the auxiliary field method
• Tests of the envelope theory for three-body forces
• Bounds for Hamiltonians with arbitrary kinetic parts