Quantum Engi Q and A_Part_23

# Quantum Engi Q and A_Part_23 - 5.5 MULTIPLE-PARTICLE...

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Unformatted text preview: 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 finding it somewhere with spin up is integraltext | Ψ + | 2 d 3 vectorr , and the total probability of finding it somewhere with spin down is integraltext | Ψ − | 2 d 3 vectorr . The sum of the two integrals must be one to express the fact that the probability of finding the particle somewhere, either with spin 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 radicalBig ( Ψ | Ψ ) to be one. Answer: As a corresponding question in the previous subsection discussed; the total proba- bility of finding the particle somewhere with spin up is integraltext | Ψ + | 2 d 3 vectorr , and the total probability 68...
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Quantum Engi Q and A_Part_23 - 5.5 MULTIPLE-PARTICLE...

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