Further developments for the auxiliary field method

Abstract

The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles, it is shown that the approximate eigenvalues can be written as the sum of the kinetic operator evaluated at a mean momentum $p_0$ and of the potential energy computed at a mean distance $r_0$. The quantities $p_0$ and $r_0$ are linked by a simple relation depending on the quantum numbers of the state considered and are determined by an equation which is linked to the generalized virial theorem. The (anti)variational character of the method is discussed, as well as its connection with the perturbation theory. For a nonrelativistic kinematics, general results are obtained for the structure of critical coupling constants for potentials with a finite number of bound states.

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References in corpus (10)

• Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation
• A general comparison theorem
• Light baryon masses in different large-$N_c$ limits
• Semirelativistic Hamiltonians and the auxiliary field method
• Some equivalences between the auxiliary field method and the envelope theory
• Extensions of the auxiliary field method to solve Schrödinger equations
• Duality relations in the auxiliary field method
• Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials
• Critical strength of attractive central potentials
• Binding energies of semirelativistic N-boson systems

Cited by in corpus (4)

• An upper bound for asymmetrical spinless Salpeter equations
• The auxiliary field method in quantum mechanics
• Approximate solutions for N-body Hamiltonians with identical particles in D dimensions
• Bounds for Hamiltonians with arbitrary kinetic parts