Qualitative features of quantized gravitation

幸男 菊地

Derar Altarawneh, Eyad Hasan Hasan

David Harris, Craig M. Savage

We analyze a type of cavity, or trap, for atoms: a hollow optical fiber bent into a vertical U shape. The atoms are confined by gravity and by light forces due to the evanescent wave on the fiber's interior surface. A unique feature of this cavity is its mechanical flexibility, which allows tailoring of the gravitational potential experienced by the atoms. In particular a cycloid shape gives simple harmonic motion along the fiber. It can achieve confinement times similar to the parabolic reflector type of gravitational cavity. Quantized motion and an intracavity cooling scheme are considered.

F. Károlyházy

Todd S. Garon, Nelia Mann, Ellen M. McManis

We use old quantization to predict features of the energy spectrum for bound states in spherically symmetric potentials. We review the application of this method to simple quantum mechanical systems with known analytic results and show that old quantization, while not generally capable of predicting the exact quantum-mechanical spectrum, does consistently give useful information. We then apply the method to a logarithmic potential and compare the results with a numerically calculated spectrum. Finally, we use these techniques to predict the number of bound states in the Yukawa potential and again compare the results with those obtained numerically. In all cases old quantization provides good predictive power for the main features of the true quantum-mechanical problem, and thus can serve as a “back-of-the-envelope” technique for providing rough, qualitative information about the system.

D.V. Ahluwalia