- #1
Graham87
- 63
- 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!
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!
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.
The non-zero entries!Graham87 said:Where in the matrix did you not agree ?
Thanks! Just noticed my error.PeroK said:The non-zero entries!
The concept of matrix representations in quantum mechanics involves representing physical quantities such as position, momentum, and energy as matrices. This allows for the mathematical description of quantum systems and their behavior.
Matrix representations are used in quantum mechanics to describe the state of a quantum system, calculate probabilities of different outcomes, and predict the evolution of the system over time. They also allow for the calculation of observables, such as energy and momentum, from the system's wave function.
Matrix representations provide a mathematical framework for understanding and predicting the behavior of quantum systems. They allow for the calculation of probabilities and observables, which can be compared to experimental results. They also provide a way to visualize and manipulate complex quantum systems.
Matrix representations are closely related to other mathematical concepts in quantum mechanics, such as wave functions, operators, and eigenvalues. They provide a way to connect these concepts and make predictions about the behavior of quantum systems.
While matrix representations are a powerful tool in quantum mechanics, they do have limitations. They can only be applied to systems with a finite number of states and may not accurately describe systems with continuous variables. Additionally, the calculations involved in matrix representations can become complex and time-consuming for larger systems.