Discovering A^2: Attachment with Question and Solution Included

[Pruddy]

please check the attachment below. The question and the attempted solution is found there. Thanks a lot for your help in advance.

 

[HallsofIvy]

I have great difficulty reading this but it appears that you are integrating the function A (sin(2pi/L) x from 0 to L. That a rather trivial integral. Are you sure it isn't A sin((2pi/L) x)= A sin(2pi x/L)?

You also have "x" in your final answer. Since this is a definite integral, evaluated for x equal to the limits of integration, there should be no "x" in the result.

 

[Pruddy]

Thank you so much hallsoflvy for your reply. I am very grateful! I have attached a new picture to this email. I am looking for the value of A when the function is equal to zero. The final answer is sqrt (2/L). I want to understand the steps and how they got the final answer. Thanks so much in advance!

 

[Ray Vickson]

please check the attachment below. The question and the attempted solution is found there. Thanks a lot for your help in advance.

Your attachment is essentially unreadable. Why not adhere to PF standards and just type out the problem and your proposed solution?

 

[Kidiz]

Your attachment is essentially unreadable. Why not adhere to PF standards and just type out the problem and your proposed solution?

Doing this would also help future readers, in case your picture gets deleted or something.

 

[Pruddy]

Hey Ray, please look at the updated attachment below. I have tried to edit the old one but don't see any button that would allow me do so. Thanks so much for your help in advance! :)

 

[Kidiz]

Hey Ray, please look at the updated attachment below. I have tried to edit the old one but don't see any button that would allow me do so. Thanks so much for your help in advance! :)

The $X$ is most likely an argument of the function $\sin$, that is, it should be inside the brackets. Why are you studying quantum mechanics without doing calculus first? You should definitely study calculus before. This is the simplest math you'll encounter.

But answering your question:

https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus#Corollary

 

[HallsofIvy]

Once again, you have not completed the integral- evaluate it at the two limits of integration and subtract. After that it should be easy to solve the equation for A.