Use of Lambert's Theorem for the n-Dimensional Coulomb Problem

Details Use of Lambert's Theorem for the n-Dimensional Coulomb Problem Use of Lambert's Theorem for the n-Dimensional Coulomb Problem

2009-06-07

arxiv.org/abs/0906.1338v1

Phys. Rev. A vol. 80 p. 012101 (2009)

Physics

Quantum Physics

11 pages, 7 figures. Accepted in Phys. Rev. A

Scientific paper

10.1103/PhysRevA.80.012101

We present the analytical solution in closed form for the semiclassical limit of the quantum mechanical Coulomb Green 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 function is found to be an excellent approximation to the quantum mechanical Green function.

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