Relativistic extension of the Kay-Moses method for constructing transparent potentials in quantum mechanics

Journal Article · Mon Feb 01 04:00:00 EST 1993 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.47.897· OSTI ID:6729856

Toyama, F M ^[1]; Nogami, Y; Zhao, Z ^[2]

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1. Institute of Computer Sciences, Kyoto Sangyo University, Kyoto 603 (Japan)
2. Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1 (Canada)

For the Dirac equation in one space dimension with a potential of the Lorentz scalar type, we present a complete solution for the problem of constructing a transparent potential. This is a relativistic extension of the Kay-Moses method which was developed for the nonrelativistic Schroedinger equation. There is an infinite family of transparent potentials. The potentials are all related to solutions of a class of coupled, nonlinear Dirac equations. In addition, it is argued that an admixture of a Lorentz vector component in the potential impairs perfect transparency.

• OSTI ID: 6729856
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 47:2; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ENERGY LEVELS
EQUATIONS
FUNCTIONS
NEGATIVE ENERGY STATES
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
POTENTIALS
SCHROEDINGER EQUATION
WAVE EQUATIONS
WAVE FUNCTIONS