  A method is presented to compute approximate solutions for eigenequations in
quantum mechanics with an arbitrary kinetic part. In some cases, the
approximate eigenvalues can be analytically determined and they can be lower or
upper bounds. A semiclassical interpretation of the generic formula obtained
for the eigenvalues supports a new definition of the effective particle mass
used in solid state physics. An analytical toy model with a Gaussian dependence
in the momentum is studied in order to check the validity of the method.
