A closed formula for the barrier transmission coefficient in quaternionic quantum mechanics

Author(s)

De Leo, Stefano ^[1] ; Ducati, Gisele ^[2] ; Leonardi, Vinicius ^[1] ; Pereira, Kenia ^[1]

Affiliation

^[1] Univ Estadual Campinas, Dept Appl Math, BR-13083970 Campinas, SP - Brazil

^[2] Fed Univ ABC, CMCC, BR-09210170 Santo Andre, SP - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 51, n. 11 NOV 2010.
• Web of Science Citations: 3

Abstract

In this paper, we analyze, by using a matrix approach, the dynamics of a nonrelativistic particle in presence of a quaternionic potential barrier. The matrix method used to solve the quaternionic Schrodinger equation allows us to obtain a closed formula for the transmission coefficient. Up to now, in quaternionic quantum mechanics, almost every discussion on the dynamics of nonrelativistic particle was motivated by or evolved from numerical studies. A closed formula for the transmission coefficient stimulates an analysis of qualitative differences between complex and quaternionic quantum mechanics and by using the stationary phase method, gives the possibility to discuss transmission times. (c) 2010 American Institute of Physics. {[}doi:10.1063/1.3504165] (AU)

• FAPESP's process: 10/02216-2 - The wave packet formalism in the study of differential equations in quantum mechanics and optics
• Grantee: Stefano de Leo
• Support Opportunities: Scholarships abroad - Research