What is the real component of complex products in quantum mechanics?

[kasse]

$$Re [e^{iE_{0}t/\hbar} \cdot e^{-iE_{1}t/\hbar}] = Re[ e^\frac{it}{\hbar}(E_{0}-E_{1})] = cos \frac{t}{\hbar}(E_{o}-E_{1})$$

Correct?

 

[Mark44]

Check your multiplication. You ended up with two terms, each with two factors. You should have ended up with four terms, each with two factors.

Another approach is to multiply the two exponentials first before converting them to cos X + i sin X. Remember that e^A * e^B = e^(A + B).

 

[kasse]

I've updated it. Is this what you meant?

 

[Mark44]

That's what I meant in "another approach." Also, your answer looks to be correct this time.