Semirelativistic Hamiltonians and the auxiliary field method

Abstract

Approximate analytical closed energy formulas for semirelativistic Hamiltonians of the form $\sigma \sqrt{{\mathbf{p}}^2+m^2}+V(r)$ are obtained within the framework of the auxiliary field method. This method, which is equivalent to the envelope theory, has been recently proposed as a powerful tool to get approximate analytical solutions of the Schrödinger equation. Various shapes for the potential $V(r)$ are investigated: power-law, funnel, square root, and Yukawa. A comparison with the exact results is discussed in detail.

References in corpus (10)

• On two- and three-body descriptions of hybrid mesons
• Constituent gluon interpretation of glueballs and gluelumps
• Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation
• Excited flux tube from $q\bar{q}g$ hybrid mesons
• Some equivalences between the auxiliary field method and the envelope theory
• Extensions of the auxiliary field method to solve Schrödinger equations
• Upper limit on the critical strength of central potentials in relativistic quantum mechanics
• Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials
• Unified Treatment of Mixed Vector-Scalar Screened Coulomb Potentials for Fermions
• Auxiliary field method for the square root potential