- #1
Homo Novus
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Homework Statement
Consider the angular momentum operator [itex]\vec{J_{y}}[/itex] in the subspace for which j=1. Write down the matrix for this operator in the usual basis (where [itex]J^{2}[/itex] and [itex]J_{z}[/itex] are diagonal). Diagonalize the matrix and find the eigenvalues and orthonormal eigenvectors.
Homework Equations
[itex]\vec{J} = \vec{L} + \vec{S}[/itex] (total angular momentum)
The Attempt at a Solution
I know J is the sum of angular momentum, L, and spin angular momentum, S, but how to we get it in matrix form? Spin would just be [itex]\hbar / 2[/itex] times the y Pauli matrix... but how do we express L in matrix form? Also, I really don't understand how to obtain eigenvalues and eigenvectors... Could someone go through the problem for me? Textbook is Griffiths. Thanks in advance.