Someone argues: "Hydrogen's ground state is a bound Coulomb state

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Approximation methods · Approximation methods

Deriving the Spectrum, Ch Atoms in electric fields

Problem

Someone argues: "Hydrogen's ground state

1s

is a bound Coulomb state, so treat it by degenerate perturbation theory exactly as for

n=2

. Reusing that level's result, the

1s

state should split linearly into two components at

\pm3ea_0\mathcal E

. For

\mathcal E=1.0\times10^7\,\mathrm{V\,m^{-1}}

this gives shifts of

\pm3ea_0\mathcal E \approx \pm1.6\times10^{-3}\,\mathrm{eV}

, far larger than any quadratic estimate." ((a)) Find the error in this reasoning. ((b)) State the correct order of magnitude of hydrogen's

1s

shift at this field.