(a)
The discussion based on Equation 7.118 when
(a)
Answer to Problem 7.54P
Form Equation 7.118 when
Explanation of Solution
From Equation 7.118,
The sum of the manifestly real and then the above equation is precisely Equation 7.15.
Write Equation 7.15,
Therefore,
The second-order correction to the energy is the term of order
Where,
Solving the terms separately from equation (I),
Solving for
Divide equation (III) in (II) to solve for
Solving further,
Using Equation 7.13,
Therefore,
Substituting in Equation (II), the second-order correction of the
Conclusion:
Form Equation 7.118 when
(b)
Show that
(b)
Answer to Problem 7.54P
It has been prove that
Explanation of Solution
The first-order expectation value of
Given, the expectation value of
Therefore,
Hence proved.
For one-dimensional oscillator, Equation 3.114
Solving for
Substitute the above equation in equation (IV)
The classical answer for the polarizability is also
Conclusion:
It has been prove that
(c)
The expectation value of
(c)
Answer to Problem 7.54P
The expectation value of
Explanation of Solution
The first order expectation value of
Solving the terms in the above equation separately for simplicity, using Equation 2.70,
Therefore,
And,
Solving the terms inside the bracket in equation (VI) by using Equation 2.67 repeatedly,
And
Therefore,
Similarly solving for equation (VII),
And
Therefore,
Therefore, equation (VI) and (VII) becomes,
And,
Substitute the above equations in equation (V)
Conclusion:
Thus, the expectation value of
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Chapter 7 Solutions
Introduction To Quantum Mechanics
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