Integrals of motion and quantum operators for hydrogenic atoms in external fields
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Date
2000Type
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Abstract
We report five cases of integrability for a hydrogenic atom under three static external fields: a magnetic field, an electric field, and a van der Waals interaction. Exact integrals of motion and corresponding quantum operators are obtained explicitly for each case. Integrals of motion (quantum operators) can be expressed as components of a suitably generalized Runge-Lenz vector (operator). Quadratic quantum operators are found to have the amazing property of requiring a nonclassical extra term ...
We report five cases of integrability for a hydrogenic atom under three static external fields: a magnetic field, an electric field, and a van der Waals interaction. Exact integrals of motion and corresponding quantum operators are obtained explicitly for each case. Integrals of motion (quantum operators) can be expressed as components of a suitably generalized Runge-Lenz vector (operator). Quadratic quantum operators are found to have the amazing property of requiring a nonclassical extra term proportional to h². The structuring of the classical phase space is investigated numerically via Poincare surfaces of section and corroborates the analytical results. ...
In
Physical review. A, Atomic, molecular, and optical physics. New York. Vol. 62, no. 4 (Oct. 2000), 043410 12p.
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Foreign
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