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Relationship Between the Probability Current and Continuity Equation

  1. Mar 6, 2013 #1
    I'm currently reading through a textbook by David Miller and attempting to teach myself quantum mechanics to assist with my electrical engineering. I have run into a little trouble trying to understand how the probability current satisfies the continuity equation with a probability distribution as shown:

    (The probability current equation that is defined in the textbook is given in the attached image)

    (d/dt)P(x,t) + (d/dx)J(x,t) = 0, where P(x,t) = |ψ(x,t)|^2

    This is an assumption made in deriving further applications about the probability current and the text suggests that I derive the relationship to practice the mathematics of quantum mechanics but I can't see how the expression is valid.
    Any ideas on how to go about it? Thanks.

    Attached Files:

  2. jcsd
  3. Mar 6, 2013 #2
    I would suggest by starting with the probability, write the probability as [itex]\psi^* \psi[/itex], and take the time derivative. Make connection with the Schrödinger equation after that.
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