Homework #1 Part 1 (Due January 18
th
, 2011)
Please show all work on a separate sheet of paper.
1.
Show that e
αx
is an eigenfunction of the operator . What is the eigenvalue? (2 pts)
2.
Why is it impossible to solve Schrodinger’s Equation for systems with two or more
electrons? (2pts.)
3.
Write out a theoretical Be
2
electron configuration symbolically [ex: H
2
= (σ1s)
2
]. (1 pt)
4.
We can reduce the energy expression for a theoretical wavefunction, φ, by using linear
combinations of other wavefunctions, Ψ, as shown below.
Can be simplified to :
where c
n
is given by:
Subtracting the ground state energy of the system, E
0
, from either side of the simplified
energy expression gives us:
Finally, here comes the question: Explain why the right side of this equation is always
positive, proving that E
φ
≥ E
0
as the variational principle states (2 pts).
5.
Given the probability densities below, what is the significance of lower curvature in the
σbonding case vs. the individual Ψ
A
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 Fall '09
 Atom, Atomic orbital, molecular orbital diagram, Walsh Diagram

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