### Abstract

We develop a systematic approach to determine the large {pipe}p{pipe} behavior of the momentum-space wave function, φ{symbol}(p), of a one-dimensional quantum system for which the position-space wave function, ψ(x), has a discontinuous derivative at any order. We find that if the kth derivative of the potential energy function for the system has a discontinuity, there is a corresponding discontinuity in ψ^{(k+2)}(x) at the same point. This discontinuity leads directly to a power-law tail in the momentum-space wave function 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.

Original language | English (US) |
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Article number | 025011AJP |

Pages (from-to) | 94-102 |

Number of pages | 9 |

Journal | American Journal of Physics |

Volume | 79 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2011 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*American Journal of Physics*,

*79*(1), 94-102. [025011AJP]. https://doi.org/10.1119/1.3492723