Calculating Probability Current for Free Particles

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SUMMARY

The discussion focuses on calculating the probability current for free particles in quantum mechanics, specifically using the formula involving the wave function and its complex conjugate. The user seeks clarification on the distinction between the wave function (psi) and its complex conjugate (psi*), as well as how to derive the probability current from the time-dependent wave function. The key takeaway is that understanding the properties of complex numbers is essential for manipulating wave functions in quantum mechanics.

PREREQUISITES
  • Basic understanding of quantum mechanics principles
  • Familiarity with wave functions and their properties
  • Knowledge of complex numbers and their conjugates
  • Experience with calculus, particularly derivatives
NEXT STEPS
  • Study the derivation of the probability current formula in quantum mechanics
  • Learn about the properties of complex functions and their conjugates
  • Explore time-dependent wave functions for free particles in quantum mechanics
  • Review calculus techniques for differentiating complex functions
USEFUL FOR

Undergraduate students in physics, particularly those studying quantum mechanics, as well as educators and anyone seeking to deepen their understanding of wave functions and probability currents.

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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