Show that by astute choice of the adjustable parameters
Answer to Problem 8.25P
It has been prove that by astute choice of the adjustable parameters
Explanation of Solution
The Normalization condition
Solve for
Substitute the above equation in equation (I) to find the value of
Write the Hamiltonian of the given system
Then,
Where,
The first term inside the bracket in equation (III) is
Thus, equation (III) becomes
From the above equation, the expectation value of
Solving the terms inside the bracket separately,
But,
Therefore, equation (IV) becomes,
Solve the expectation value of
Where,
Solving for
Solving further,
Solving for
Solving further,
Therefore,
The expectation value of the Hamiltonian becomes,
Solving the above equation,
At
The expectation value,
Hence proved.
Conclusion:
It has been prove that by astute choice of the adjustable parameters
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Chapter 8 Solutions
Introduction To Quantum Mechanics
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