Effect of confining potential on information entropy measures in hydrogen atom: extensive and non-extensive entropy

A spherically confined hydrogen atom has been considered using two different confined potentials such as modified Kratzer and non-spherical oscillator potentials. First, the Schrödinger equation in r-space has been solved and the exact analytical wave functions and energy levels have been obtained. Then, the Renyi entropy and Shannon entropy in r-space have been calculated. In addition, we have numerically calculated the wave functions in p-space by performing Fourier transform. The calculations have been done for different quantum numbers n and l and also quantum size r₀. The Bialynicki–Birula–Mycielski inequality is also tested. It is found that this inequality depends on non-extensive parameter q. (author)