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Classical limit of quantized Kepler motion

Tadashi Toyoda

AIP conference proceedingsJan 1, 20000 citations

Binomial potential of the electron-proton interaction as an alternative to the Coulomb law

V. K. Gudym, E. V. Andreeva

It is shown that a solution of the classical Kepler problem with a binomial potential explains the stationary orbits of the hydrogen atom, its discrete spectrum, and trajectories of scattered electrons with energies from several electron-volts to relativistic values. The Schrodinger equation with the binomial potential takes the form of a classical wave equation. Hence, the binomial potential is a more appropriate model for understanding atomic phenomena than the model based on the Coulomb potential.It is shown that a solution of the classical Kepler problem with a binomial potential explains the stationary orbits of the hydrogen atom, its discrete spectrum, and trajectories of scattered electrons with energies from several electron-volts to relativistic values. The Schrodinger equation with the binomial potential takes the form of a classical wave equation. Hence, the binomial potential is a more appropriate model for understanding atomic phenomena than the model based on the Coulomb potential.

Journal of Surface Investigation X-ray Synchrotron and Neutron TechniquesApr 1, 20072 citations

Natural relationship between classical orbits and quantum Hamiltonians for the Kepler problem

Jason D. Tran, Leanne Doughty, James K. Freericks

Central force problems involve coupled linear differential equations of motion. By decoupling the differential equations, we show how to efficiently solve for the orbits of the Kepler problem without any complicated integrals. Introducing quantization provides a deep connection between the solution for these classical orbits and the quantum Hamiltonian of hydrogen for states that have definite total angular momentum.

American Journal of PhysicsApr 22, 20251 citation

Quantization in Hamiltonian particle mechanics

Ebbe Thue Poulsen

Lecture notes in mathematicsJan 1, 19741 citation

The Quantization of Relativistic Classical Mechanics

Herbert C. Corben

Physics EssaysSep 1, 19951 citation

Stabilization of Rydberg atoms against photoionization

Lambertus D. Noordam

We have observed that the amount of photoionization from an atomic Rydberg state with a pulsed laser depends critically on the length of the pulse, whereas lowest-order perturbation theory implies that the yield depends only on the fluence (the integrated intensity) of the pulse. We have measured the yield for one-photon ionization with short (0.5–2.7-ps) high-intensity laser pulses from the 27d Rydberg state in barium. With equal fluence, the yield decreases for pulses shorter than the Kepler orbit time of the outer electron (2.2 ps) because not all of its wave function comes near the core during the length of the pulse. The observations and this classical picture are confirmed by quantum-mechanical calculations.We have observed that the amount of photoionization from an atomic Rydberg state with a pulsed laser depends critically on the length of the pulse, whereas lowest-order perturbation theory implies that the yield depends only on the fluence (the integrated intensity) of the pulse. We have measured the yield for one-photon ionization with short (0.5–2.7-ps) high-intensity laser pulses from the 27d Rydberg state in barium. With equal fluence, the yield decreases for pulses shorter than the Kepler orbit time of the outer electron (2.2 ps) because not all of its wave function comes near the core during the length of the pulse. The observations and this classical picture are confirmed by quantum-mechanical calculations.

May 8, 19940 citations

Stationary Kepler orbits of the electron with velocity-dependent perturbations — classical quantization

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Stationary Kepler orbits of the electron with velocity-dependent perturbations — classical quantization

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