Special comparison theorem for the Dirac equation

Abstract

If a central vector potential V(r,a) in the Dirac equation is monotone in a parameter 'a', then a discrete eigenvalue E(a) is monotone in 'a'. For such a special class of comparisons, this generalizes an earlier comparison theorem that was restricted to node free states. Moreover, the present theorem applies to every discrete eigenvalue.

3 pages

References in corpus (2)

• Spectral Comparison Theorem for the Dirac Equation
• Solutions to the 1d Klein-Gordon equation with cutoff Coulomb potentials

Cited by in corpus (10)

• Relativistic Comparison Theorems
• A general comparison theorem
• Comparison theorems for the Klein-Gordon equation in d dimensions
• Comparison theorems for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions
• Refined comparison theorems for the Dirac equation in d dimensions
• Nodal theorems for the Dirac equation in d >= 1 dimensions
• Dirac eigenvalues for a softcore Coulomb potential in d dimensions
• Nature Itself in a Mirror Space-Time
• Sharp comparison theorems for the Klein--Gordon equation in $d$ dimensions
• General comparison theorems for the Klein-Gordon equation in d dimensions