Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
نویسنده
چکیده
We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized Pöschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudoHermiticity are also discussed. PACS: 02.20.Sv; 03.65.Fd; 03.65.Ge
منابع مشابه
Non-Hermitian Hamiltonians with real and complex eigenvalues: An sl(2,C) approach
Potential algebras are extended from Hermitian to non-Hermitian Hamiltonians and shown to provide an elegant method for studying the transition from real to complex eigenvalues for a class of non-Hermitian Hamiltonians associated with the complex Lie algebra A1.
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The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra sl(2,C) or A1. This leads to new types of both PTsymmetric and non-PT-symmetric Hamiltonians. PACS: 02.20.Sv, 03.65.Fd, 03.65.Ge
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