Complex square well - a new exactly solvable quantum mechanical model

Citation
Cm. Bender et al., Complex square well - a new exactly solvable quantum mechanical model, J PHYS A, 32(39), 1999, pp. 6771-6781
Citations number
5
Categorie Soggetti
Physics
Journal title
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
ISSN journal
03054470 → ACNP
Volume
32
Issue
39
Year of publication
1999
Pages
6771 - 6781
Database
ISI
SICI code
0305-4470(19991001)32:39<6771:CSW-AN>2.0.ZU;2-C
Abstract
Recently, a class of PT-invariant quantum mechanical models described by th e non-Hermitian Hamiltonian H = p(2) + x(2)(ix)(epsilon) was studied It was found that the energy levels for this theory are real for all epsilon grea ter than or equal to 0. Here, the limit as epsilon --> infinity is examined . It is shown that in this limit, the theory becomes exactly solvable. A ge neralization of this Hamiltonian, H = p(2) + x(2M)(ix)(epsilon) (M = 1, 2, 3,...) is also studied, and this PT-symmetric Hamiltonian becomes exactly s olvable in the large-epsilon limit as well. In effect, what is obtained in each case is a complex analogue of the Hamiltonian for the square-well pote ntial. Expansions about the large-epsilon limit are obtained.