Quantum phase space for the one-dimensional hydrogen atom on the hyperbola

We obtain the solution of the one-dimensional hydrogen atom on the hyperbola by transforming its Schr�dinger equation into the modified P�schl-Teller equation. We write explicitly the wave functions both in configuration and momentum space, and check the contraction limit of the system to the flat space model. Finally, we find the closed form of the Wigner function for the states of this system. � 2005 American Institute of Physics