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|
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(2.19) |
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|
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(2.20) |
We assume the single particle levels to be non-degenerate. Still, the two-electron level
is degenerate because it corresponds to the two states
(
for the symmetric and
for the anti-symmetric state. The corresponding two-by-two matrix of
we need diagonalise for the degenerate first order perturbation theory in the sub-space spanned by
is however diagonal so that things become easy:
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(2.21) |
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(2.22) |
Exercise: Show that
.
The explicit calculation of the remaining diagonal elements
and
yields
Exercise: Verify these expressions.
The symmetrical orbital wave function (
) belongs to the
(singlet) spinor, whereas the anti-symmetrical orbital wave function (
) belongs to the
(triplet) spinors. Therefore, the unperturbed energy level
splits into two levels
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(2.25) |
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(2.26) |