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How to get wavelength of the wave function?

  1. Aug 20, 2013 #1
    A particle in the infi nite square well potential is found at the 3-rd excited state. What is the
    wavelength of the wave function of the particle?
    this is a mcq from my faculty who denoted the correct answer to be 2/3 a ...how to get that ?
     
  2. jcsd
  3. Aug 20, 2013 #2
    The wave function is a sine function that goes to zero at the boundaries of a region of length a.

    Therefore, there must be an integral (1, 2, 3...) number of half-wavelengths in a region a.

    That is, a = integer*wavelength/2, or wavelength = 2a/integer.

    For the ground state, the integer = 1, for the second excited state the integer = 3. It seems that the examiner has misread the question when giving the answer.
     
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