Upper limit on the number of bound states of the spinless Salpeter equation

Abstract

We obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the ultrarelativistic case ($m=0$), for the existence of at least one $\ell$-wave bound states: $C(\ell ,p/(p-1))$ ${\int }_0^{\infty }dr{r}^{p-1}|V^{-}(r){|}^p\ge 1$, where $C(\ell ,p/(p-1))$ is a known function of $\ell$ and $p>1$.

18 pages

References in corpus (5)

• Light Meson Spectra and Instanton Induced Forces
• Energy bounds for the spinless Salpeter equation: harmonic oscillator
• 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

Cited by in corpus (8)

• The Salpeter equation and probability current in the relativistic Hamiltonian quantum mechanics
• The relativistic massless harmonic oscillator
• Necessary and sufficient conditions for existence of bound states in a central potential
• The Spinless Relativistic Woods-Saxon Problem
• The modified fundamental equations of quantum mechanics
• Upper limit on the critical strength of central potentials in relativistic quantum mechanics
• On the coherent states for a relativistic scalar particle
• Analytical Solution of two-body spinless Salpeter Equation for Hellmann Potential