Use of Lambert's theorem for the n-dimensional Coulomb problem

Journal Article · Wed Jul 15 00:00:00 EDT 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.012101· OSTI ID:21313195

Kanellopoulos, Vassiliki ^[1]; Kleber, Manfred ^[1]; Kramer, Tobias ^[2]

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1. Department of Physics (T30), Technische Universitaet Muenchen, James-Franck-Str., 85747 Garching (Germany)
2. Institute for Theoretical Physics, Universitaet Regensburg, 93040 Regensburg (Germany)

We present the analytical solution in closed form for the semiclassical limit of the quantum-mechanical Coulomb Green's function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and which allows us to treat the system as an essentially one-dimensional problem. The semiclassical result assumes a simple analytical form and is well suited for a numerical evaluation. The method can also be extended to classically forbidden space regions. Already for moderately large principal quantum numbers {nu}{>=}5, the semiclassical Green's function is found to be an excellent approximation to the quantum-mechanical Green's function.

• OSTI ID: 21313195
• Journal Information: Physical Review. A, Vol. 80, Issue 1; Other Information: DOI: 10.1103/PhysRevA.80.012101; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
EVALUATION
GREEN FUNCTION
NUMERICAL ANALYSIS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM MECHANICS
QUANTUM NUMBERS
SEMICLASSICAL APPROXIMATION
SPACE