1. Wavefunctions and Bound Systems
Chapters Q9,10 (3rd ed)

2. What’s a Wavefunction? y y H = E
Looking a head -Schroedinger’s Equation: y y
H = E
Wavefunction “psi” solves Schroedinger’s equation and contains, in its components, all of the information we need to determine values of observables…

3. Wavefunctions are only part of the story…
The information in the wavefunction is “coded” in its components. Actual values for observables depend on “how you ask” the wavefunction
Operators tell us what we want to know:
Example: momentum
Classical:
Quantum:
This is not as strange as it seems – you got used to thinking of momentum as “em” times “vee” – this is just another way to think about it!

4. example (cont…) Consider a free particle traveling in space…
An eigenvalue equation
Eigenvalue for momentum
Momentum operator
Wavefunction (eigenfunction)

5. What wavefunctions are (and are not!)
Wavefunctions are mathematical ideas that depict probability distributions (Born interpretation)
Wavefunctions can be described using the mathematics of waves but are not “real”
Wavefunctions obey strict mathematical rules:
continuous, differentiable, finite

6. Consider the wave function below:
This is the wavefunction
This is the probability distribution

7. Applications…
Particle in a Box
Quantized Spring!
Bohr Atom

8. Molecular Examples of Particle in a Box…

9. From Carrots to Quantum Physics!
Why are carrots orange?

10. beta Carotene and Cyanine
Bond length 0.14 nm
# bonds 6
Level n = 3  4
b-Carotene ?
# bonds 18
Level n = 9  10

11. How a quanton is “bound” depends on the Potential Energy Function V(x)
V(x) is where the chemistry happens!
The Shape of the potential sets the shape of possible wavefunctions (energy eigenfunctions)
Energy Eigenfunctions are stationary states (ie – standing waves!)

12. Three Potentials in Chp 10
“Box”
“Spring”
“Coulomb”
The quanton’s wavefunction must “fit” within these potentials – that sets l and hence the energy and momentum of the quanton

13. Suggested Study Problems from Chp 10
Q10B.1, Q10B.4, Q10M.4