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Yoni V
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Homework Statement
Let ##\left|\psi\right\rangle## be a non-degenerate stationary state, i.e. an eigenstate of the Hamiltonian. Suppose the system exhibits symmetry for time inversion, but not necessarily for rotations. Show that the expectation value for the angular momentum operator is zero.
Homework Equations
The Attempt at a Solution
I'm trying to write the mathematical implications for each of the above statements, e.g. $$T(-iH)T^{-1}=iH,\; R(iH)R^{-1}=iH$$ where R,T are the corresponding unitary and anti unitary operators, and H is the Hamiltonian.
But I really don't see where this leads me. This is the beginning of the semester, so I still have very little intuition about how to take advantage of different properties such as unitarity, symmetries and commutation relations...