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The Hamiltonian of a relativistic partide can be approximated by.
p²
H= +V+H}
2m
where
H³ = -
Using first order time-independent perturbation theory.
show that the 1 order energy correction is given by
E₁=
(E²-2E <V) + <V²>)
where the expectation values are taken
the unperturbed (and undegenerate) state
P²
2m
p4
8m3c2
2mc²
14) + V14>= E|VY
with respect to
lys that satisfies

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