Calculate total energy of the system for both cases

[36 points] Two non-interacting identical particles with mass ?? are in the onedimensional harmonic oscillator potential of frequency ??. If one particle is in the
ground state, and the other in the first excited state,
a) construct the symmetric and anti-symmetric wave functions for this twoparticle system.
b) Calculate the total energy of the system for both cases (i.e. for both
symmetric and anti-symmteric wave functions)
c) Calculate the expectation value of the square of the distance between the
particles <(??1 – ??2
)
2

for both cases. Comment on your results.

1. [36 points] Consider two non-interacting electrons, with mass ??, in a onedimensional infinite square well potential of width ??. Determine the energy, and
   the normalized wave function (space and spin parts together) of the system, as
   well as the degeneracy for the
   a) ground state of the system,
   b) first excited state of the system,
   c) second excited state of the system.