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4. Write down the time-independent Schrӧdinger Equation for two non-interacting identical particles in the infinite square...

4. Write down the time-independent Schrӧdinger Equation for two non-interacting identical particles in the infinite square well. Assuming the spins of the two particles are parallel to each other, i.e., all spin-up, find the normalized wave function representing the ground state of the two-particle system and the energies for the two cases:

(a) Two particles are identical bosons.

(b) Two particles are identical fermions.

and

(c) Find the wave functions and energies for the first and second excited states for the two-boson and two-fermion systems.

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