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- Title
Sharp comparison theorems for the Klein-Gordon equation in dimensions.
- Authors
Hall, Richard L.; Zorin, Petr
- Abstract
We establish sharp (or 'refined') comparison theorems for the Klein-Gordon equation. We show that the condition , which leads to , can be replaced by the weaker assumption which still implies the spectral ordering . In the simplest case, for , , or and for , , or . We also consider sharp comparison theorems in the presence of a scalar potential (a 'variable mass') in addition to the vector term (the time component of a four-vector). The theorems are illustrated by a variety of explicit detailed examples.
- Subjects
KLEIN-Gordon equation; GROUND state (Quantum mechanics); POTENTIAL theory (Physics); VARIABLE mass systems; RELATIVISTIC effects in atoms
- Publication
International Journal of Modern Physics E: Nuclear Physics, 2016, Vol 25, Issue 6, p-1
- ISSN
0218-3013
- Publication type
Article
- DOI
10.1142/S0218301316500397