Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Relationship Between the Probability Current and Continuity Equation
  1. Probability Current (Replies: 1)

Loading...