(Solution) - Two identical spin fermions move in one dimension under the -(2025 Original AI-Free Solution)

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Two identical spin ½ fermions move in one dimension under the influence of the infinite-wall potential V = ? for x < 0, x > L, and V = 0 for 0 ? x ? L.
a. Write the ground-state wave function and the ground-state energy when the two particles are constrained to a triplet spin state (ortho state).
b. Repeat (a) when they are in a singlet spin state (para state).
c. Let us now suppose that the two particles interact mutually via a very short-range attractive potential that can be approximated by V= ? ??(x1 ? x2) (? > 0). Assuming that perturbation theory is valid even with such a singular potential, discuss semi quantitatively what happens to the energy levels obtained in (a) and (b).