Shannon information entropy for an infinite circular well

• We study the Shannon information entropies for the infinite circular well.
• The Fourier transform of Bessel functions is obtained analytically for any m.
• The position entropy SrSr increases with the radius R for a given m.
• The Bialynicki-Birula–Mycielski (BBM) inequality is tested.

We study the position SrSr and momentum SpSp Shannon entropies of the infinite circular well and find that the SrSr increases with the radius R for a given m, but first increases and then decreases with the m for a given R  . The variation SpSp on radius R is from the first increment to the final decrement, but its general tendency first decreases with m   and then increases with it. We also note that the variation of SrSr on radius R is almost independent of n. Finally, BBM inequality is tested and hold for this system.