  We develop a systematic approach to determine the large |p| behavior of the
momentum-space wavefunction, phi(p), of a one-dimensional quantum system for
wich the position-space wavefunction, psi(x), has a discontinuous derivative at
any order. We find that if the k-th derivative of the potential energy function
has a discontinuity, there is a corresponding discontinuity in psi^{(k+2)}(x)
at the same point. This discontinuity leads directly to a power-law tail in the
momentum-space wavefunction proportional to 1/p^{k+3}. A number of familiar
pedagogical examples are examined in this context, leading to a general
derivation of the result.
