An electron in a hydrogen-like atom occupies the orbital angular momentum state (a…

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Symmetry, angular momentum and spin · Symmetry, angular momentum and spin

The Structure of Quantum Mechanics, Ch Angular momentum from the rotation group

Problem

An electron in a hydrogen-like atom occupies the orbital angular momentum state ∣l=1,m=0⟩|l=1,m=0\rangle (a pzp_z orbital). The atom is rotated by β=2π/3\beta = 2\pi/3 about the yy axis. Using d1,0(1)(β)=−sin⁡β2,d0,0(1)(β)=cos⁡β,d−1,0(1)(β)=sin⁡β2,d^{(1)}_{1,0}(\beta) = -\frac{\sin\beta}{\sqrt2},\quad d^{(1)}_{0,0}(\beta) = \cos\beta,\quad d^{(1)}_{-1,0}(\beta) = \frac{\sin\beta}{\sqrt2}, find the probability that a subsequent measurement of LzL_z gives each of +ℏ+\hbar, 00, −ℏ-\hbar.

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