Some equivalences between the auxiliary field method and the envelope theory

Abstract

The auxiliary field method has been recently proposed as an efficient technique to compute analytical approximate solutions of eigenequations in quantum mechanics. We show that the auxiliary field method is completely equivalent to the envelope theory, which is another well-known procedure to analytically solve eigenequations, although relying on different principles \textit{a priori}. This equivalence leads to a deeper understanding of both frameworks.

v2 to appear in J. Math. Phys

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• Duality relations in the auxiliary field method
• Eigenstates with the auxiliary field method
• Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials
• Approximate solutions for N-body Hamiltonians with identical particles in D dimensions
• Further developments for the auxiliary field method
• Bounds for Hamiltonians with arbitrary kinetic parts
• Potential envelope theory and the local energy theorem