IJPAM: Volume 67, No. 2 (2011)

THE BLACK-SCHOLES EQUATION AND
CERTAIN QUANTUM HAMILTONIANS

Juan M. Romero$^1$, O. González-Gaxiola$^{2}$, J. Ruiz de Chávez$^3$,
R. Bernal-Jaquez$^4$
$^{1,2,4}$Department of Applied Mathematics and Systems
Universidad Autónoma Metropolitana - UNIDAD Cuajimalpa
Artificios 40, México, D.F., 01120, MEXICO
$^1$e-mail: jromero@correo.cua.uam.mx
$^2$e-mail: ogonzalez@correo.cua.uam.mx
$^4$e-mail: rbernal@correo.cua.uam.mx
$^{3}$Department of Mathematics
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