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Two identical spin-1/2 particles are confined to an infinite one-dimensional square well of width a with infinite potential barriers at x=0 and x=a. The potential is V(x)=0 for 0 <= x <= a. Suppose that the particles interact weakly by the potential V_1(x)=Kdelta(x_1 - x_2), where x_1 and x_2 are the positions of the two particles , K is a constant, and delta is the Dirac delta function. This represents a very short-range weak force between the two particles.
a) Using first-order perturbation theory, find the perturbation to the energy of the lowest-energy singlet state.
b) Show that the first-order perturbation to the energy of the lowest-energy triplet state is zero.
c) What is the physical reason for the answer in part (b)?
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