  Since the advent of quantum mechanics different approaches to find analytical
solutions of the Schr\"odinger equation have been successfully developed. Here
we follow and generalize the approach pioneered by Natanzon and others by which
the Schr\"odinger equations can be transformed into another well-known equation
for transcendental function (e.g., the hypergeometric equation). This sets a
class of potentials for which this transformation is possible. Our
generalization consists in finding potentials allowing the transformation of
the Schr\"odinger equation into a triconfluent Heun equation. We find the
energy eigenvalues of this class of potentials, the eigenfunction and the exact
superpartners.
