The correction to the ground state energy of hydrogen due to the finite size of the nucleus.
Answer to Problem 7.33P
The correction to the ground state energy of hydrogen due to the finite size of the nucleus is
Explanation of Solution
Using perturbation theory,
And the energy correction is
The wave function of the ground state is
Where
Solving equation (II),
Solving further,
Let
Therefore, the above equation becomes,
Solving the above equation,
Since, the ground state energy of the hydrogen is
Where
Therefore,
Keeping only the leading term,
Substitute
The energy correction for the fine structure is
Therefore, the estimated correction to the ground state energy of hydrogen due to the finite size of the nucleus is very small compared to the fine structure and the hyperfine structure.
Conclusion:
Thus, the correction to the ground state energy of hydrogen due to the finite size of the nucleus is
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Chapter 7 Solutions
INTRO TO QUANTUM MECHANICS
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