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Probability Current

  1. Jul 21, 2007 #1
    I am confused about the the probability density equation:

    [tex] \vec j = \frac{\hbar}{2mi}\left(\Psi^* \vec \nabla \Psi - \Psi \vec \nabla \Psi^*\right)[/tex]

    Psi is not a ket on the right side, correct?
    If not how can perform a del on it and get a vector on the right side?

    Can someone give me a concret example of what you would plug in to this expression:
    [tex]\Psi^* \vec \nabla \Psi [/tex]
     
  2. jcsd
  3. Jul 21, 2007 #2

    Gokul43201

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    Psi is not a ket, it is a position-space wavefunction, given by the inner product: [itex]\psi _n(x) = \langle x|n \rangle [/itex]

    E.g., in the 1D infinite square well of width L, [itex]\psi_n(x)=\sqrt{2/L}~sin(n \pi x/L) [/itex]

    The gradient of a scalar field is a vector field.
     
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