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In an introductory textbook of Quantum Mechanics, I found the momentum eigenfunction in position space to be given as Ne^ipx/h.

Where N is the normalization factor and i is root of -1.

I don't understand clearly what this function signifies. Does it tell us that the ampitude of finding a particle with momentum p oscialltes as we move about the positon / x axis?

So is it that a particle is favoured to have certain momentum values in some special positions?

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    $\begingroup$ 1. If you are in position space, why does your function not depend on $x$? 2. We can use MathJax here. 3. Why would you think it signifies anything other than any other wavefunction? 4. Try to compute $N$, and be prepared to be confused. $\endgroup$
    – ACuriousMind ♦
    Commented Jul 12, 2015 at 19:15
  • $\begingroup$ Sorry, for the typo, it does have the position term. $\endgroup$
    – Normie
    Commented Jul 12, 2015 at 19:17
  • $\begingroup$ The probability to find the particle in a position depends on the MAGNITUDE of the wave function, which in this case is constant. ACuriosMind is correct, though, the proper normalization in this case is not a constant but the Dirac delta function, at least that's the lie we teach to our children, otherwise we would have to walk them trough a proper treatment of continuous linear operator spectra, which is a whole series of lectures for mathematicians. $\endgroup$
    – CuriousOne
    Commented Jul 12, 2015 at 19:33

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A particle with such a wave function is in a momentum eigenstate i.e. all measurements of momentum for the particle will always return the value p. The physically relevant quantity with respect to position is the amplitude modulus squared which by the Born interpretation gives us the probability of finding the particle at a given point. In this case, this probability turns out to be constant, which basically means a particle with precise momentum value can be absolutely anywhere with regard to position. This is in accordance with the Heisenberg uncertainty principle. Since uncertainty in p is 0, uncertainty in x is infinite, thus the particle can be found absolutely anywhere in space.

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