Abstract

We point out some striking similarities between three simple, yet fundamental, quantum systems: (1) the two-dimensional isotropic oscillator, (2) the two-dimensional hydrogen atom, and (3) the lossless two-port beam splitter. By using the quantum theory of angular momentum, we obtain the unitary transformation connecting the Cartesian and polar eigenfunctions of the two-dimensional oscillator. By similar methods, we also obtain the unitary transformation connecting the polar and parabolic eigenfunctions of the two-dimensional hydrogen atom. Finally, we show that both the preceding transformations are closely related to the unitary transformation that connects the input and output photon statistics at a lossless 50-50 beamsplitter. Thus, a close connection is established between the quantum beam splitter, recently studied by several workers^1,2 and two basic quantum systems.

© 1990 Optical Society of America