Franz Schwabl Quantum Mechanics 4th Edit · Problem 13.1

Several-Electron Atoms

Physics — Quantum Mechanics · helium-angular-integral

Problem

The following formula is used in computing the ground-state energy shift of helium (see Eq.\ (13.24)): ∫dΩ1 dΩ2 1∣x1−x2∣=(4π)21max⁡(r1,r2).\int d\Omega_1\, d\Omega_2\,\frac{1}{|\boldsymbol{x}_1 - \boldsymbol{x}_2|} = (4\pi)^2 \frac{1}{\max(r_1,r_2)}. (a) Derive this formula.

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