- #1

t0pquark

- 14

- 2

- Homework Statement
- Compute the probability that a measurement of ##L_x## will give zero for an angular momentum particle (1) with ##\vert \psi \rangle = \begin{bmatrix} \frac{2}{3} \\ \frac{1}{3} \\

\frac{-2}{3} \end{bmatrix} ##.

- Relevant Equations
- In a 3D Hilbert space, for spin 1, ##L_x = \frac{\hbar}{2} \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 1\\ 0 & 1 & 0 \end{bmatrix}##.

The probability that a measurement of ##L_x## will give zero for a given ##\psi## should be ##\vert \langle L_x = 0 \vert \psi \rangle \vert ^2##, I think.

I found the eigenvalues of ##L_x## to be ##\lambda = -1, 0, 1##. Since it asks for the probability that the measurement will give zero, I think I should be looking at the eigenvector that corresponds to zero, which is ##\begin{bmatrix} \frac{1}{\sqrt 2} \\ 0 \\ \frac{-1}{\sqrt 2} \end{bmatrix} ##.

I am not sure where to go from here?

I found the eigenvalues of ##L_x## to be ##\lambda = -1, 0, 1##. Since it asks for the probability that the measurement will give zero, I think I should be looking at the eigenvector that corresponds to zero, which is ##\begin{bmatrix} \frac{1}{\sqrt 2} \\ 0 \\ \frac{-1}{\sqrt 2} \end{bmatrix} ##.

I am not sure where to go from here?