Classical representation for hydrogen atom in s-states. (English) Zbl 1423.81078
Summary: A classical representation for hydrogen atom in bound \(s\)-states is developed. In this representation, the Schrödinger equation takes a form of balance equation with respect to some virtual exchange between classical states with energies \(\epsilon\) and \(\mu\) due to sub-barrier penetration. Possible application of the classical representation in the calculation of inelastic transitions in the collision of an electron with a hydrogen atom by the classical trajectory Monte Carlo method is discussed.
MSC:
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
| 81Q65 | Alternative quantum mechanics (including hidden variables, etc.) |
| 81V45 | Atomic physics |
| 81U05 | \(2\)-body potential quantum scattering theory |
| 65C05 | Monte Carlo methods |
Keywords:
classical-quantum correspondence; classical representation; Abel transform; solvable problemsReferences:
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