Matrix representation for (S1+S2)^2 operator

In summary, the conversation is about a problem with deriving a matrix using two different methods. The person is looking for help in figuring out what went wrong and is also open to receiving the matrix without the detailed derivation. The link provided describes the problem in more detail.
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I've derived the matrix using two different, but equivalent methods (the one described in the above link-Sakurai and by calculating the direct products of Pauli matrices) and it came out the same, yet its eigenvalues are not what I know they must be, so there must be something fundamentally wrong in my procedure, but I just can't detect it. If you happen to know how the matrix looks like without a detailed derivation, I'd be grateful for that too, cause I'm really stuck here :frown:
 

1. What is the matrix representation for (S1+S2)^2 operator?

The matrix representation for (S1+S2)^2 operator is a 4x4 matrix, where the diagonal elements are the sum of the squares of the individual operators (S1^2 + S2^2) and the off-diagonal elements are the cross products of the individual operators (S1*S2 + S2*S1).

2. How is the matrix representation for (S1+S2)^2 operator derived?

The matrix representation for (S1+S2)^2 operator is derived by using the properties of matrix multiplication and the commutation relations between the individual operators S1 and S2. It involves expanding the expression (S1+S2)^2 and simplifying it to obtain the 4x4 matrix.

3. What does the matrix representation for (S1+S2)^2 operator represent?

The matrix representation for (S1+S2)^2 operator represents the square of the sum of two operators, which is a common operation in quantum mechanics. It can be used to calculate the expectation value of the operator or to find the eigenvalues and eigenvectors of the operator.

4. Can the matrix representation for (S1+S2)^2 operator be extended to higher powers?

Yes, the matrix representation for (S1+S2)^2 operator can be extended to higher powers by using the properties of matrix multiplication. However, as the power increases, the size of the matrix also increases, making it more complex to work with.

5. How is the matrix representation for (S1+S2)^2 operator used in quantum mechanics?

The matrix representation for (S1+S2)^2 operator is used in quantum mechanics to represent the square of the sum of two operators, which is a common operation in calculating physical quantities. It can also be used to study the properties of a system and to solve quantum mechanical equations.

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