Multidimensional WKB approximation for particle tunneling
- Department of Chemical Physics and Optics, Charles University, Faculty of Mathematics and Physics, Ke Karlovu 3, 121 16 Prague 2 (Czech Republic) and Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada)
A method for obtaining the WKB wave function describing the particle tunneling outside of a two-dimensional potential well is suggested. The Cartesian coordinates (x,y) are chosen in such a way that the x axis has the direction of the probability flux at large distances from the well. The WKB wave function is then obtained by simultaneous expansion of the wave function in the coordinate y and the parameter determining the curvature of the escape path. It is argued, both physically and mathematically, that these two expansions are mutually consistent. It is shown that the method provides systematic approximation to the outgoing probability flux. Both the technical and conceptual advantages of this approach in comparison with the usual approach based on the solution of classical equations of motion are pointed out. The method is applied to the problem of the coupled anharmonic oscillators and verified through the dispersion relations.
- OSTI ID:
- 20718227
- Journal Information:
- Physical Review. A, Vol. 72, Issue 2; Other Information: DOI: 10.1103/PhysRevA.72.024101; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ANHARMONIC OSCILLATORS
CARTESIAN COORDINATES
COMPARATIVE EVALUATIONS
DISPERSION RELATIONS
DISTANCE
EQUATIONS OF MOTION
EXPANSION
HARMONIC OSCILLATORS
MATHEMATICAL SOLUTIONS
POTENTIALS
PROBABILITY
TUNNEL EFFECT
TWO-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS
WKB APPROXIMATION