Ground-State Wigner Function for the D-dimensional Hydrogen Atom

Let X and k, respectively, be the position and momentum vectors in D-dimensional space, and let r and k be the corresponding hyperradii  

We may then introduce spherical polar coordinates of x by the defi- 

A similar representation exists, of course, for the vector k. For the volume element, dx, we have the expression  

Integrating over all angles gives the total solid angle  

With the above notation at hand, we may now specify the form of the position-space wavefunction V o(x) for the ground state of the f -dimensional hydrogen atom, [3]  

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