Complex 
square well - a new exactly solvable quantum 
mechanical model

doi:10.1088/0305-4470/32/39/305

Complex square well - a new exactly solvable quantum mechanical model

Carl M Bender et al 1999 J. Phys. A: Math. Gen. 32 6771-6781 doi: 10.1088/0305-4470/32/39/305

PDF (212 KB) | Gzipped PS (209 KB) | References | Articles citing this article

Carl M Bender

, Stefan Boettcher

, H F Jones§ and Van M Savage

Department of Physics, Washington University, St Louis, MO 63130, USA

Department of Physics, Emory University, Atlanta, GA 30322, USA
§ Blackett Laboratory, Imperial College, London SW7 2BZ, UK

Abstract. Recently, a class of calP calT -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+x^2M(ix) (M = 1,2,3, ... ) is also studied, and this calP calT -symmetric Hamiltonian becomes exactly solvable 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 potential. Expansions about the large- epsilon limit are obtained.

Print publication: Issue 39 (1 October 1999)
Received 21 June 1999

Post to CiteUlike |

Post to Connotea |

Post to Bibsonomy

Complex square well - a new exactly solvable quantum mechanical model

Find related articles

Article options

Authors & Referees