
(a)
The first-order correction to the ground state,
(a)

Answer to Problem 7.56P
The first-order correction to the ground state,
Explanation of Solution
Write the expression for the first-order correction to the ground state
Solving the above equation by multiply and divide by
Where,
The above equation becomes,
Substitute
Conclusion:
Thus, the first-order correction to the ground state,
(b)
Show that
(b)

Answer to Problem 7.56P
This has been proved that
The value of the two integrals,
Explanation of Solution
The degenerate first-excited states are
The Hamiltonian is invariant when the
Dropping the complex conjugation as the orbitals are real. And interchange
Here,
Where,
Where,
Let
Substituting the above equation in equation (III)
Substituting the above equation in equation (II),
Using variable substitute, where
Similarly solve for
Where,
Solving further,
Substitute the above equation in equation (IV)
Solving further,
Substitute equation (IV) and (VI) in (I),
The energies are
Similarly for the symmetric spatial state of parahelium
The calculated value is in agreement with the results from Figure 5.1 by predicting that orthohelium is lower in energy.
Conclusion:
It has been proved that
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Chapter 7 Solutions
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