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Angular_Momentum_and_Spin

Angular_Momentum_and_Spin - Angular Momentum and Spin I...

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Angular Momentum and Spin 1 I: Hydrogen atoms, angular momenta, and probabilities Ignoring spin (for now), an electron is known to be in a hydrogen atom state given by ψ ( t = 0) = r 1 6 R 10 Y 0 0 + r 1 6 R 21 Y 1 1 + cR 32 Y 1 2 A. Pick a value of c which normalizes the wavefunction. Is the value unique? (Why/why not?) B. What possible outcomes (with what associated probabilities) are there for a measurement of energy? C. Does your answer above depend on the time you wait before measuring energy? D. Consider the state given by ˆ . Is it in any sense the “outcome” of a physical measurement of energy on our state ψ ? X Check your results with a tutorial instructor. PHYS 3220 Tutorials 2009 c S. Pollock, S. Goldhaber, and the Physics Education Group University of Colorado, Boulder
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Angular Momentum and Spin 2 Continuing with the previous page, with (still) ψ ( t = 0) = r 1 6 R 10 Y 0 0 + r 1 6 R 21 Y 1 1 + cR 32 Y 1 2 E. What possible outcomes (with what associated probabilities) are there for a measurement of ˆ L 2 ? F. What possible outcomes (with what associated probabilities) are there for a measurement of ˆ L z ? G. Does your answer above depend on the time you wait before measuring ˆ L z ? PHYS 3220 Tutorials 2009 c S. Pollock, S. Goldhaber, and the Physics Education Group University of Colorado, Boulder
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Angular Momentum and Spin 3 H. Suppose you start in the state (from the previous page)
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