Question

Discuss (qualitatively) the energy level scheme for helium if (a) electrons were identical bosons, these "electrons" still have spin 1/2, so the spin configurations are the singlet and the triplet.

Answer 1

Electrons were identical in this case electrons are treated as bosons the wave function of any system is given by psi = psi (a) psi (s) were psi(a) is the spetal part and psi(s) is the spin part psi should be symmetric for bosons the spatial part of the ground state wave function is psi_0 (r^bar_1, r^bar_2) = psi_100(r^bar_1) psi_100(r^bar_2) = 8/pi a^3 e^-2 (r^bar_1 + r^bar_2)/a therefore from it is clear that psi (r^bar_1, r^bar_2) = psi_0 (r^bar_2, r^bar_1) this the ground state is spatially symmetric so ist goes with the symmetric configuration. \r\n this the ground state is orthob = and it is degenerate as we know both the ground state end all united states come in both ortho and para form we don't know which goes with the symmetric spatial configuration that we do not have prior knowledge as to whether ortho (or) para has higher energy.