Upper limit on the critical strength of central potentials in relativistic quantum mechanics

Abstract

In the context of relativistic quantum mechanics, where the Schrödinger equation is replaced by the spinless Salpeter equation, we show how to construct a large class of upper limits on the critical value, $g_{\mathrm{c}}^{(\ell )}$, of the coupling constant, $g$, of the central potential, $V(r)=-gv(r)$. This critical value is the value of $g$ for which a first $\ell$-wave bound state appears.

arXiv comment8 pages

References in corpus (11)

• Unified description of light- and strange-baryon spectra
• Light Meson Spectra and Instanton Induced Forces
• Energy bounds for the spinless Salpeter equation: harmonic oscillator
• Discrete Spectra of Semirelativistic Hamiltonians
• Discrete spectra of semirelativistic Hamiltonians from envelope theory
• A unified meson-baryon potential
• Upper and lower limits for the number of S-wave bound states in an attractive potential
• Energy bounds for the spinless Salpeter equation
• Integral equation formulation of the spinless Salpeter equation
• Upper limit on the number of bound states of the spinless Salpeter equation
• Lower limit in semiclassical form for the number of bound states in a central potential

Cited by in corpus (7)

• An upper bound for asymmetrical spinless Salpeter equations
• Semirelativistic Hamiltonians and the auxiliary field method
• The auxiliary field method in quantum mechanics
• Auxiliary field method and analytical solutions of the Schrödinger equation with exponential potentials
• Deformed Morse-like potential
• Existence of mesons after deconfinement
• General form of the covariant field equations of arbitrary spin and the relativistic canonical quantum mechanics