Fund Quantum Mechanics Lect & HW Solutions 85

Fund Quantum Mechanics Lect & HW Solutions 85 - up or...

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5.5. MULTIPLE-PARTICLE SYSTEMS INCLUDING SPIN 67 Answer: s ( s + 1)¯ h 2 = 15 4 ¯ h 2 . 5.5 Multiple-Particle Systems Including Spin 5.5.1 Wave function for a single particle with spin 5.5.1.1 Solution complexsa-a Question: What is the normalization requirement of the wave function of a spin 1 / 2 particle in terms of Ψ + and Ψ ? Answer: The particle must be found somewhere, either with spin up or with spin down. The total probability of Fnding it somewhere with spin up is i | Ψ + | 2 d 3 vr , and the total probability of Fnding it somewhere with spin down is i | Ψ | 2 d 3 vr . The sum of the two integrals must be one to express the fact that the probability of Fnding the particle somewhere, either with spin
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Unformatted text preview: up or spin down, must be one, certainty. 5.5.2 Inner products including spin 5.5.2.1 Solution complexsai-a Question: Show that the normalization requirement for the wave function of a spin 1 / 2 particle in terms of Ψ + and Ψ − requires its norm r a Ψ | Ψ A to be one. Answer: As a corresponding question in the previous subsection discussed; the total proba-bility of Fnding the particle somewhere with spin up is i | Ψ + | 2 d 3 vr , and the total probability...
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This note was uploaded on 01/06/2012 for the course PHY 3604 taught by Professor Dr.danielarenas during the Fall '11 term at UNF.

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