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# 10.P: Exercises

1. Demonstrate that the particle interchange operator, , in a system of two identical particles is Hermitian.

2. Consider two identical spin- particles of mass confined in a cubic box of dimension . Find the possible energies and wavefunctions of this system in the case of no interaction between the particles.

3. Consider a system of two spin- particles with no orbital angular momentum (i.e., both particles are in -states). What are the possible eigenvalues of the total spin angular momentum of the system, as well as its projection along the -direction, in the cases in which the particles are non-identical and identical?