Show that a variation theory treatment of
Interpretation:
The variation theory treatment of
Concept introduction:
According to the variation theory, the lower the energy of a system the better is the approximation. Variation theory is based on the fact that any test system has average energy equal to or greater than the ground state energy of that system. The advantage of the variation theory is that any wavefunction can be taken for any test system.
Answer to Problem 12.44E
The variation theory treatment of
Explanation of Solution
The expression for trial function can be written as given below.
Substitute the values in the above expression as follows.
The above equation can be simplified as given below.
Solve the integral as follows.
The value of
Substitute this value in the expression for trial energy as given below.
The exact energy of hydrogen atom in ground state is given by the expression written below.
From the above equation it is clear that the exact energy of hydrogen atom in ground state is same as the minimized trial energy.
The variation theory treatment of
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