Does \(A e^{iA} = e^{iA} A\)?

Thread starter russdot
Start date Oct 26, 2009
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Operators

AI Thread Summary

The discussion centers on whether the equation \(A e^{iA} = e^{iA} A\) holds true when A is an operator. It is clarified that since \(e^{A}\) is defined by a power series, and A commutes with itself, it follows that A also commutes with \(e^{A}\). This implies that the original equation is valid under the given conditions. The conversation emphasizes the importance of understanding the properties of operators in relation to exponential functions. Overall, the conclusion is that the equation is indeed correct.

Oct 26, 2009

russdot

If A is an operator, is it correct/allowed to say:
Ae^{iA} = e^{iA}A

Thanks

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Oct 26, 2009

Ben Niehoff

Science Advisor

Gold Member

Think of how e^{A} is defined.

Oct 26, 2009

russdot

Ah yes, so since e^{A} is defined with a power series e^{A} = 1 + A + \frac{A^{2}}{2!} + \frac{A^{3}}{3!} + ... and A commutes with itself then A would commute with e^{A}
Thanks!

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