(adsbygoogle = window.adsbygoogle || []).push({}); 1. Problem:

Consider Hydrogen in its ground state in a magnetic field of magnitudeB.

Compute the effect of the magnetic field on the hyperfine structure of Hydrogen

(that is you should include the interaction of both the proton and electron magnetic

moments with the applied magnetic field). Give the values of the energy eigenvalues

for B = 1 gauss and for B = 10^{4}gauss.

2. Relevant equations

the hamiltonian for a dipole moment is H=-μB

μ_{p}=g_{p}eS_{p}/2m_{p}

μ_{e}=-eS_{e}/m_{e}

F=J+Iwhere F is the atom's total angular momentum

3. The attempt at a solution

well, i think that the Hamiltonian looks like:

H=μ_{e}B+_{p}B(_{ext}μ+_{e}μ)_{p}

so do we just act this H on the ground state wave function?

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# Homework Help: Hyperfine Splitting In A Magnetic Field

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