- #1
Rahmuss
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Homework Statement
Just a snipit of one of my homework problems. I'm trying to find out what [tex]\Psi \frac{\partial \Psi^{*}}{\partial x}[/tex] equals to help me find out what the probability current for a given free particle is.
Homework Equations
[tex]\Psi = Ae^{i(kx-\frac{\hbar k^{2}t}{2m})}[/tex]
The Attempt at a Solution
I view [tex]\Psi^{*}[/tex] as the complex part of the given wave function; but in this case there is no real part, it's all complex. Does that mean the real part is zero? If so then [tex]\Psi \frac{\partial \Psi^{*}}{\partial x} = 0[/tex]. If [tex]\Psi = \Psi^{*}[/tex], then the larger equation I'm trying to calculate comes out to be zero because it's:
[tex]\Psi \frac{\partial \Psi^{*}}{\partial x} - \Psi^{*} \frac{\partial \Psi}{\partial x}[/tex]
So what am I missing here? Does it actually have a zero probability current because it's a "free particle" (whatever that really means)?