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