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

Bagchi, B.; Quesne, C.

doi:10.1016/S0375-9601(00)00512-0

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

Aug, 2000

14 pages

Published in:

Phys.Lett.A 273 (2000) 285-292

e-Print:

math-ph/0008020 [math-ph]

DOI:

10.1016/S0375-9601(00)00512-0

Report number:

ULB-229-CQ-00-4

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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.

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