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Probability density from Wave Function

  1. Jan 9, 2013 #1
    A friend of mine recently tried to tell me that the square of the wave function for a particle (that is, [itex]\Psi^2[/itex]) gives the probability density of finding a particle in space.

    I disagree. I always thought that the wave function multiplied by its complex conjugate (that is, [itex]\Psi \Psi^*[/itex]) yielded the probability density for the particle. They are definitely not the same, because [itex]\forall a,b \neq 0, \ (a+bi)^2 = a^2 + 2abi + b^2 \neq a^2 + b^2[/itex].

    So, is the probability density given by [itex]\Psi^2[/itex] or [itex]\Psi \Psi^* = |\Psi|^2[/itex]?
  2. jcsd
  3. Jan 9, 2013 #2
    It's the [itex]|\Psi|^2[/itex], a real number
  4. Jan 11, 2013 #3

    Jano L.

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    Gold Member

    Perhaps your friend referred to wave function that is eigenstate of some atomic or molecular Hamiltonian. These can be chosen to be real, so then ##\Psi^2## gives the correct density as well as ##|\Psi|^2##. But the latter is the general expression.
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