In this problem you will prove that the ground-state energy for a system obtained using the variational
Question:
a. The approximate wave function Φ can be expanded in the true (but unknown) eigenfunctions Ï n of the total energy operator in the form Φ = ΣncnÏn. Show that by substituting Φ = ΣncnÏn in the equation
you obtain the result
b. Because the Ïn are eigenfunctions of HÌ, they are orthonormal and HÌÏn = EnÏn. Show that this information allows us to simplify the expression for D from part (a) to
c. Arrange the terms in the summation such that the first energy is the true ground-state energy E0 and the energy increases with the summation index m. Why can you conclude that E E0 ¥ 0?
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