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

M. Belloni, R. W. Robinett

Research output: Contribution to journalArticle

5 Scopus citations

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/pk+3. A number of familiar pedagogical examples are examined in this context, leading to a general derivation of the result.

Original languageEnglish (US)
Article number025011AJP
Pages (from-to)94-102
Number of pages9
JournalAmerican Journal of Physics
Volume79
Issue number1
DOIs
StatePublished - Jan 2011

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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