Question

The matrix representations of the $S_x$ and $S_y$ operators are $S_x = \frac{\hbar}{\sqrt{2}} \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}$ $S_y = \frac{\hbar}{\sqrt{2}} \begin{pmatrix} 0 & -i & 0 \\ i & 0 & -i \\ 0 & i & 0 \end{pmatrix}$

          The matrix representations of the $S_x$ and $S_y$ operators are
$S_x = \frac{\hbar}{\sqrt{2}} \begin{pmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix}$
$S_y = \frac{\hbar}{\sqrt{2}} \begin{pmatrix} 0 & -i & 0 \\ i & 0 & -i \\ 0 & i & 0 \end{pmatrix}$

The matrix representations of the Sx and Sy operators are
Sx = (ħ)/(√(2))
< p m a t r i x >
Sy = (ħ)/(√(2))
< p m a t r i x >

Added by Christopher E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sarita Rana

Step 1

First, let's find the eigenvalues. The eigenvalues of a matrix are the values λ for which the equation (A - λI)x = 0 has a non-zero solution. Here, A is the matrix representation of the Sx operator and I is the identity matrix. So, we need to solve the Show more…

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Quantum Mechanics I: Diagonalize the Sx and Sy operators in the spin-1 case to find the eigenvalues and the eigenvectors of both operators. The matrix representations of the Sx and S, operators are /0 1 0 h 1 0 1 0 1 /0 /0 -i 0 h i 0 -i 0 i 0/