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Normalizing a Wave Function

  • #1

Homework Statement



ψ(x,t) = Ae^(-λ|x|)e^(-iωt)

This is a rather long problem so I won't get into the details. I understand how to normalize, and most of the rest of the problem. I also have the solutions manual. I just need an explanation of why this goes to Ae^(-2λ|x|). I can't figure it out.

Homework Equations



I can't think of any that make sense to use.

The Attempt at a Solution



I believe it is because you can add the powers of exponentials, such that e^(x)e^(x) = e^(2x). I do not understand how you can just get rid of the imaginary, angular frequency, or time parts...

Any explanation would be great.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618

Homework Statement



ψ(x,t) = Ae^(-λ|x|)e^(-iωt)

This is a rather long problem so I won't get into the details. I understand how to normalize, and most of the rest of the problem. I also have the solutions manual. I just need an explanation of why this goes to Ae^(-2λ|x|). I can't figure it out.

Homework Equations



I can't think of any that make sense to use.

The Attempt at a Solution



I believe it is because you can add the powers of exponentials, such that e^(x)e^(x) = e^(2x). I do not understand how you can just get rid of the imaginary, angular frequency, or time parts...

Any explanation would be great.
It's because to normalize you need to integrate ψψ*, the wave function times its complex conjugate. The complex conjugate of e^(-iωt) is e^(iωt). e^(-iωt)*e^(iωt)=e^0=1.
 
  • #3
Ah okay. I had thought it might have something to do with the complex conjugate.

So for the complex conjugate you just get...

e^(-λ|x|)*e^(-λ|x|) = e^(-2λ|x|)
 
Last edited:
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Ah okay. I had thought it might have something to do with the complex conjugate.

So for the complex conjugate you just get...

e^(-λ|x|)*e^(-λ|x|) = e^(-2λ|x|)
Sure.
 

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