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Three-Dimensional Problems — Nouredine Zettili
Physics — Quantum Mechanics · eigenvalues-l2-lz-spherical-harmonics
Problem Find the eigenvalues of the operators L ^ 2 \hat{L}^2 L ^ 2 L ^ z \hat{L}_z L ^ z Y 21 ( θ , φ ) Y_{21}(\theta,\ \varphi) Y 21 ( θ , φ ) Y 3 , − 2 ( θ , φ ) Y_{3,-2}(\theta,\ \varphi) Y 3 , − 2 ( θ , φ ) 1 2 [ Y 33 ( θ , φ ) + Y 3 , − 3 ( θ , φ ) ] \frac{1}{\sqrt{2}}\left[Y_{33}(\theta,\ \varphi) + Y_{3,-3}(\theta,\ \varphi)\right] 2 1 [ Y 33 ( θ , φ ) + Y 3 , − 3 ( θ , φ ) ] Y 40 ( θ , φ ) Y_{40}(\theta,\ \varphi) Y 40 ( θ , φ ) Browse the problem library