Carl M Bender et al 1999 J. Phys. A: Math. Gen. 32 6771 doi:10.1088/0305-4470/32/39/305
Complex square well - a new exactly solvable quantum mechanical model
Carl M Bender
, Stefan Boettcher
, H F Jones§ and Van M Savage
Recently, a class of 
-invariant quantum mechanical models described by the non-Hermitian Hamiltonian H = p2+x2(ix)
was studied. It was found that the energy levels for this theory are real for all 
0. Here, the limit as 
is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, H = p2+x2M(ix) (M = 1,2,3, ... ) is also studied, and this -symmetric Hamiltonian becomes exactly solvable in the large- limit as well. In effect, what is obtained in each case is a complex analogue of the Hamiltonian for the square-well potential. Expansions about the large- limit are obtained.
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Issue 39 (1 October 1999)
Received 21 June 1999
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Complex square well - a new exactly solvable quantum mechanical model
Carl M Bender et al 1999 J. Phys. A: Math. Gen. 32 6771
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