Classical limit of quantized Kepler motion

Michał Aleksander Gryziński

Jan Mostowski

Ivaïlo M. Mladenov

Vassil V. Tsanov, Ivaïlo M. Mladenov

Piotr Garbaczewski, Dariusz Prorok

We establish a manifest connection between the classical and quantized versions of the Kepler problem in case of scattering states. The affinity to the four-oscillator system allows to deduce the stochastic description of the Kepler prohlem, which in the leading order of the tree (semi-classical) approximation is given in terms of three independent Markov processes the latter being driven by the classical Kepler motion.

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.