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- Consider a system consisting of two non-interacting particles, and three
one-particle states, , , and . How
many different two-particle states can be constructed if the particles are
(a) distinguishable, (b) indistinguishable bosons, or (c) indistinguishable
fermions?

- Consider two non-interacting particles, each of mass , in
a one-dimensional harmonic oscillator potential of classical oscillation
frequency . If one particle is in the ground-state, and the
other in the first excited state, calculate
assuming that the particles are (a) distinguishable, (b) indistinguishable bosons, or (c) indistinguishable fermions.

- Two non-interacting particles, with the same mass , are
in a one-dimensional box of length . What are the four lowest
energies of the system? What are the degeneracies of these
energies if the two particles are (a) distinguishable, (b) indistinguishable
bosons, or (c) indistingishable fermions?

- Two particles in a one-dimensional box of length occupy
the and states. Write the properly normalized
wavefunctions if the particles are (a) distinguishable, (b) indistinguishable
bosons, or (c) indistinguishable fermions.

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Richard Fitzpatrick
2010-07-20