  This paper present how to solve the problem of cylindrical quantum wells with
potential energy different from zero and with singularity of the energy on the
axis of the cylinder. The solution to the problem was obtained using methods of
computer algebra. The results depend of Bessel and Kummer functions. This paper
present energy levels and wave functions in some of the cases with an exactly
form and in other cases with an approximated form, this form depended on the
possibility of integrating the special functions and calculating the zeros of
these functions. Here we can see the power of the method in the applications
concerning complex problems of quantum mechanics, and the possibility of being
able to apply this method in order to solve other problems in science and also
in engineering.
