Abstract
Comparison theorems are established for the Dirac and Klein-Gordon equations. We suppose that and are two real attractive central potentials in dimensions that support discrete Dirac eigenvalues and . We prove that if , then each of the corresponding discrete eigenvalue pairs is ordered . This result generalizes an earlier, more restrictive theorem that required the wave functions to be node-free. For the the Klein-Gordon equation, similar reasoning also leads to a comparison theorem provided in this case that the potentials are negative and the eigenvalues are positive.
- Received 5 February 2010
DOI:https://doi.org/10.1103/PhysRevA.81.052101
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