1. Real eigenvalues of non-hermitian operators.
- Author
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Surján, Péter R., Szabados, Ágnes, and Gombás, András
- Subjects
- *
BLOCH equations , *MOLECULAR physics , *HERMITIAN operators , *OPERATOR equations , *QUANTUM mechanics - Abstract
A basic fact, having fundamental significance in quantum mechanics, is that hermitian (or self-adjoint) operators have only real eigenvalues. However, in certain applications in molecular physics, one deals with non-hermitian operators. We discuss a condition for non-hermitian operators to have real eigenvalues, proving that it is the case if and only if it can be decomposed as a product of two, generally non-commuting hermitian operators, one of which is positive definite. The theorem is illustrated on the example of non-hermitian effective Hamiltonians occurring in the non-perturbative form of the Bloch equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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