- #1

- 57

- 16

- Homework Statement
- See pic

- Relevant Equations
- See pic

I have found J^2 and Jz, but I am not sure how to find Jx and Jy.

I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results.

Thanks!

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- Thread starter Graham87
- Start date

In summary, the conversation is about finding the operators Jx and Jy using J+ and J- and forming a matrix with the correct entries. The conversation includes suggestions and tips on how to approach the problem and correct errors.

- #1

- 57

- 16

- Homework Statement
- See pic

- Relevant Equations
- See pic

I have found J^2 and Jz, but I am not sure how to find Jx and Jy.

I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results.

Thanks!

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- #2

- 25,774

- 17,347

Using ##J_{\pm}## sounds like a good idea. Show us what you get.Graham87 said:Homework Statement::See pic

Relevant Equations::See pic

View attachment 313615

I have found J^2 and Jz, but I am not sure how to find Jx and Jy.

I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results.

View attachment 313617

Thanks!

- #3

Mentor

- 8,345

- 5,345

You have to do it the other way around: Express ##J_x## and ##J_y## in terms of ##J_+## and ##J_-##.Graham87 said:I’m thinking maybe use J+-=Jx+-iJy ? But I get unclear results.

- #4

- 57

- 16

I got this, but it gets messy when I try to find J+- with this expression:

I don’t know how to form the matrix, what goes where.

- #5

Mentor

- 8,345

- 5,345

- #6

- 57

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Something like this?

- #7

- 25,774

- 17,347

Good effort, but I don't agree with some of the entries in the ##J_{\pm}## matrices.

- #8

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- #9

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The non-zero entries!Graham87 said:Where in the matrix did you not agree ?

- #10

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Thanks! Just noticed my error.PeroK said:The non-zero entries!

cheers!

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