Homework 1 Part 1

Homework 1 Part 1 - Homework #1 Part 1 (Due January 18th,...

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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 σ-bonding case vs. the individual Ψ A
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Homework 1 Part 1 - Homework #1 Part 1 (Due January 18th,...

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