Where did I miss a minus sign?

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SUMMARY

The discussion revolves around a homework problem involving the manipulation of exponential expressions in quantum mechanics. Participants clarify that the user did not miss a minus sign in their calculations and suggest expanding the exponentials to simplify the expression. The user confirms that upon expansion, the minus sign is recovered, indicating a correct understanding of the problem. The conversation emphasizes the importance of careful algebraic manipulation in quantum mechanics.

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Homework Statement


a.jpg


Homework Equations

The Attempt at a Solution


e.jpg


1.1st circle on the left : where did I miss a minus sign?
2. How to show that the last term is equal to 1?

Thanks!
 
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davon806 said:
1.1st circle on the left : where did I miss a minus sign?
I don't think you missed a minus sign here.
How to show that the last term is equal to 1?
You'll have to see if it is, in fact, equal to 1.

You could try expanding the two exponentials in your question-mark expression and see if you can simplify it. Think about what happens when you act on the ground state with powers of a† followed by powers of a.
 
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TSny said:
I don't think you missed a minus sign here.
You'll have to see if it is, in fact, equal to 1.

You could try expanding the two exponentials in your question-mark expression and see if you can simplify it. Think about what happens when you act on the ground state with powers of a† followed by powers of a.

Thanks, after expanding the exponential I recover the minus sign:smile:.
 
OK, good.
 

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