5.E: MultiParticle Systems (Exercises)
 Page ID
 15754

Consider a system consisting of two noninteracting particles, and three oneparticle states, \(\psi_a(x)\), \(\psi_b(x)\), and \(\psi_c(x)\). How many different twoparticle states can be constructed if the particles are (a) distinguishable, (b) indistinguishable bosons, or (c) indistinguishable fermions?

Consider two noninteracting particles, each of mass \(m\), in a onedimensional harmonic oscillator potential of classical oscillation frequency \(\omega\). If one particle is in the groundstate, and the other in the first excited state, calculate \(\langle (x_1x_2)^{\,2}\rangle\) assuming that the particles are (a) distinguishable, (b) indistinguishable bosons, or (c) indistinguishable fermions.

Two noninteracting particles, with the same mass \(m\), are in a onedimensional box of length \(a\). 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 onedimensional box of length \(a\) occupy the \(n=4\) and \(n'=3\) states. Write the properly normalized wavefunctions if the particles are (a) distinguishable, (b) indistinguishable bosons, or (c) indistinguishable fermions.
Contributors
Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)
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