Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 5.1, Problem 5.9P

(a)

To determine

The four lowest-energy configurations and their corresponding energies and degeneracies of particles of spin 12.

(b)

To determine

The four lowest-energy configurations and their corresponding energies and degeneracies of particles of spin 1.

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TRQ. 3.1 Solve completely the following Quantum problem. Need full detailed answer, equations and if possible, theory/ literature. Question: A particle of spin 1 and a particle of spin 1/2 are in a configuration for which the total spin is equal to 1/2. If one were to measure the z-component of the spin of the particle with spin = 1, what values might one get and what are the probabilities associated with those values? Use Clebsch-Gordan table. Write the total spin state |s,ms> as linear combinations of |s1, ms1> |s2, ms2> states.
PROBLEM 2. Consider a spherical potential well of radius R and depth Uo, so that the potential is U(r) = -Uo at r R. Calculate the minimum value of Uc for which the well can trap a particle with l = 0. This means that SE at Uo > Uc has at least one bound ground state at l = 0 and E < 0. At Ug = Uc the bound state disappears.
PROBLEM 2 Calculate the probability distribution of momenta p for a ld oscillator in the ground state (n = 0). Calculate the mean square dispersions (x2), (p²), and the product (r2)(p²).
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