Is this number real?

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  • #1
dyn
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Main Question or Discussion Point

hi. I have been looking at a QM example in a book. It works out the expectation value for momentum which I know should be a real number but I can't see how or why the following number is real
α and β are complex numbers with | α |2 + | β |2 = 1 and ω and t are real

-i ( α*β e-iωt -αβ*eiωt)

Can anyone tell me if this is a real number and why?
Thanks
 

Answers and Replies

  • #2
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The two parts in the bracket are the complex conjugates of each other: They have the same real component but opposite imaginary component. Their difference has a real component of zero, it is purely imaginary. If you multiply that by -i you get a real number.
 
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  • #3
dyn
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Thanks. I just couldn't see it but now I can. Thanks again
 

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