sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues

Abstract

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 $A_1$. This leads to new types of both PT-symmetric and non-PT-symmetric Hamiltonians.

LaTeX, amssym,14 pages, no figures, to be published in Phys. Lett. A

References in corpus (5)

• PT -symmetric harmonic oscillators
• A new PT symmetric complex Hamiltonian with a real spectra
• Shape invariant potentials with PT symmetry
• PT-symmetric sextic potentials
• New set of exactly solvable complex potentials giving the real energies

Cited by in corpus (93)

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