Where did I miss a minus sign?

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Homework Help Overview

The discussion revolves around a problem in quantum mechanics, specifically related to the manipulation of exponential operators and their effects on quantum states. Participants are examining a potential oversight regarding a minus sign in the calculations and the verification of a term equating to 1.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants question whether a minus sign was overlooked in the original calculations and discuss how to verify the equality of a term to 1. Suggestions include expanding exponential expressions and considering the effects of operator actions on quantum states.

Discussion Status

The discussion is ongoing, with some participants providing guidance on how to approach the verification of the term's equality. There is an indication that expanding the expressions may lead to clarification regarding the minus sign issue.

Contextual Notes

Participants are navigating the complexities of quantum mechanics and operator algebra, with an emphasis on ensuring accuracy in mathematical expressions. There is a focus on the implications of operator actions on the ground state, which may influence the understanding of the problem.

davon806
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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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