Where did I miss a minus sign?

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The discussion revolves around a homework problem where the user questions a potential missing minus sign in their calculations. Responses indicate that the minus sign is likely not missing and suggest verifying the equality of the last term by expanding the exponentials involved. The user confirms that upon expansion, they do recover the minus sign, indicating they resolved their confusion. The conversation emphasizes the importance of simplification and careful examination of expressions in mathematical problems. Overall, the issue was clarified through collaborative problem-solving.
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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.
 

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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