Thermodynamics, Statistical Physics, and Quantum Mechanics

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5.27 Three Spins (Stony Brook)

Considerthree particles of spin 1/2 which have no motion. The raising

and lowering operators of the individual

spins have the property

where the arrows indicate the spin orientation with regard to the

direction.

a) Write explicitwave functions for the four states:

b) Using the definition that construct the 4 × 4 matrices

which represent the and operators.

c) Construct the 4 × 4 matrices which represent and

d) Construct from the value of the matrix

5.28 Constant Matrix Perturbation (Stony Brook)

Consider a system described by a Hamiltonian

where andG are positive.

a) Find theeigenvalues andeigenvectors of this Hamiltonian.

b) Consider the two states

PROBLEMS