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10.P: Exercises

  1. Demonstrate that the particle interchange operator, $ P_{12}$ , in a system of two identical particles is Hermitian.

     

  2. Consider two identical spin-$ 1/2$ particles of mass $ m$ confined in a cubic box of dimension $ L$ . 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-$ 1$ particles with no orbital angular momentum (i.e., both particles are in $ s$ -states). What are the possible eigenvalues of the total spin angular momentum of the system, as well as its projection along the $ z$ -direction, in the cases in which the particles are non-identical and identical?

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