darfmore
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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.
(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.
