
Concept explainers
(a)
An upped bound on the ground state of the infinite square well using the function
(a)

Answer to Problem 8.16P
An upped bound on the ground state of the infinite square well using the function
Explanation of Solution
Given,
Normalize the above wave function,
Solving further for
The expectation value of the Hamiltonian is
Solving further,
Therefore,
Conclusion:
An upped bound on the ground state of the infinite square well using the function
(b)
The optimal value of
(b)

Answer to Problem 8.16P
The optimal value of
Explanation of Solution
Given,
Where,
Normalize the above wave function,
The expectation value of the Hamiltonian is
Solving the integral in the numerator separately for simplicity,
Substitute the above equation in equation (III),
(Using example Schaum’s 18.24)
Differentiate the above equation with respect to
Solving the above quadratic equation and the positive root is the solution that diverges at
Substituting the above relation in Equation 8.1
Conclusion:
Thus, the optimal value of
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Chapter 8 Solutions
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