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We develop a systematic approach to determine the large |p| behavior of themomentum-space wavefunction, phi(p), of a one-dimensional quantum system forwich the position-space wavefunction, psi(x), has a discontinuous derivative atany order. We find that if the k-th derivative of the potential energy functionhas 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 themomentum-space wavefunction proportional to 1/p^{k+3}. A number of familiarpedagogical examples are examined in this context, leading to a generalderivation of the result.

Less than perfect quantum wavefunctions in momentum-space: How phi(p) senses disturbances in the force