Question: The exact fine-structure formula for hydrogen (obtained from the Dirac equation without recourse to perturbation theory) is Expand to order a 4 (noting that a

The exact fine-structure formula for hydrogen (obtained from the Dirac equation without recourse to perturbation theory) is

Enj = 27-1/2 mc { [ + - - - ^ -

Expand to order a4 (noting that a

Enj = 27-1/2 mc { [ + - - - ^ - -} 1+ (j+1/2) + (j + 1/2) a,

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