IJPAM: Volume 67, No. 2 (2011)
CERTAIN QUANTUM HAMILTONIANS



R. Bernal-Jaquez


Universidad Autónoma Metropolitana - UNIDAD Cuajimalpa
Artificios 40, México, D.F., 01120, MEXICO




Universidad Autónoma Metropolitana - UNIDAD Iztapalapa
Av. San Rafael Atlixco No. 186, Col Vicentina
A.P. 55-534, 09340, Iztapalapa, Mexico, D.F., MEXICO
e-mail: jrch@xanum.uam.mx
Abstract.In this paper a quantum mechanics is
built by means of a non-Hermitian momentum operator. We have shown
that it is possible to construct two Hermitian and two non-Hermitian
type of Hamiltonians using this momentum operator. We can construct
a generalized supersymmetric quantum mechanics that has a dual based
on these Hamiltonians. In addition, it is shown that the
non-Hermitian Hamiltonians of this theory can be related to
Hamiltonians that naturally arise in the so-called quantum finance.
Received: December 18, 2010
AMS Subject Classification: 81Q12, 81Q60, 81Q65
Key Words and Phrases: quantum physics, supersymmetric quantum mechanics, quantum finance
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 2