Calculating Probability Current for Free Particles

petera88
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Hello. This is my first post here. I am an undergrad student and my first experience with quantum mechanics isn't going as well as I hoped. I decided I should join this form and ask question for conceptual help.

So here is my first question.

The formula for probability current has a psi(derivative psi*) - psi*(derivative psi).

I am trying to find it for a free particle. I know the time-dependent wave function for a free particle, and am assuming I just take the derivative and plug everything in. I think where I lack is my fundamental understanding of the wave function. So my question is...

What is the difference between the complex conjugate psi*, and just psi? To my understanding it is to take anything complex and make it real. I haven't done much work in my lower division math courses with complex numbers so don't understand if I am just given a time-dependent wave function, how to I split this to psi and psi*?
 
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I moved this to the homework section. Did not realize I was posting it here. Sorry about that.
 

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