  Quantum mechanics has about a dozen exactly solvable potentials. Normally,
the time-independent Schroedinger equation for them is solved by using a
generalized series solution for the bound states (using the Froebenius method)
and then an analytic continuation for the continuum states (if present). In
this work, we present an alternative way to solve these problems, based on the
Laplace method. This technique uses a similar procedure for the bound states
and for the continuum states. It was originally used by Schroedinger when he
solved for the wavefunctions of hydrogen. Dirac advocated using this method
too. We discuss why it is a powerful approach for graduate students to learn
and describe how it can be employed to solve all problems whose wavefunctions
are represented in terms of confluent hypergeometric functions.
