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Wave Function Terminology - Are these synonyms?

  1. Apr 4, 2014 #1
    Are the quantum mechanical terms "probability amplitude" and "probability density" used interchangeably?
  2. jcsd
  3. Apr 4, 2014 #2

    The probability amplitude is complex.
    The probability density is real.

    Take the modulus of the probability amplitude and square it to get the probability density.
  4. Apr 4, 2014 #3

    So is it safe to say that a complex wave function is a probability amplitude and that its modulus squared is a probability density?
  5. Apr 4, 2014 #4


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    Staff: Mentor

    Safe enough for all practical purposes, provided that the complex wave function in question is a solution to Schrodinger's equation.
  6. Apr 4, 2014 #5


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    Staff: Mentor

    Yes. ##\Psi## is a probability amplitude and ##\Psi^*\Psi## is the corresponding probability density, assuming that ##\Psi## has been normalized so that
    $$\int^{+\infty}_{-\infty}{\Psi^*\Psi dx} = 1$$
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