- #1
Juqon
- 31
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Homework Statement
The Hamilton-operator is given as [tex]\hat{H}[/tex] and describes the movement of a free rigid object that has the moments of inertia [tex]I_{i}[/tex]
Under what circumstances is
[tex]<\Psi|\hat{L_{1}}|\Psi> [/tex]
time-independent?
Homework Equations
[tex] \hat{H}=\frac{\hat{L_{1}^{2}}}{2I_{1}}+\frac{\hat{L_{2}^{2}}}{2I_{2}}+\frac{\hat{L_{3}^{2}}}{2I_{3}} [/tex]
[tex][\hat{L_{j}},\hat{L_{k}}]=\iota\hbar\epsilon_{jkm}\hat{L_{m}} [/tex]
[tex]<\Psi|\hat{L_{1}}|\Psi> [/tex]
The Attempt at a Solution
If it wasn't in the brac-kets, I would just try [tex]\frac{dL_{1}}{dt}=0[/tex] Also, I thought maybe I could use another picture to have the time-indepence in it automatically, but I think Schrödinger must be the right one as there the operators are constant.