1. Black Body Radiation Spectral Density Function Ave. energy of an oscillating dipole Energy emitted per unit volume, over frequency range dv at v, as a function of temperature. Energy is quantized, and proportional to frequency Classical Theory predicts that total energy emitted is infinite above 0 K

2. Photoelectric Effect Classical predictions fail to account for experimental observations slope=  =h

3. De Broglie Relation Why not for particles? For light A proton moving at 0.001 C has wavelength? A 100 g baseball moving at 10 m/s has wavelength? ~1000 times its radius

4. Diffraction

5. The Double Slit Experiment A single electron exhibits interference behaviour ???

6. Emission Spectrum of H Classical theory predicts that any orbital trajectory of an electron is unstable as it looses energy through radiation.

7. 13_01fig_PChem.jpg Energy Levels and The Boltzmann Distribution System behaves as having a continuous energy spectrum when  E≤kT

8. The Schrödinger Equation Consider the space dependent part: Recall 1 st Harmonic ie. 2 nodes (n = 2) Separable

9. The Schrödinger Equation Eigen Relationship

10. Time Dependent Schrödinger Equation The time dependent part of the wave equation Since

11. Time Dependent Schrödinger Equation Propagates the wave function through time

12. Time Dependent Schrödinger Equation ImIm ReRe tt oo roro 1 st Order D.E. Initial condition Amplitude Phase (time dependent) Space part (standing wave)

13. Propagators

14. Unitary Transformation

15. Summary

16. Quantum Mechanics for Many Particles (0,0,0) m1m1 m3m3 m2m2 m4m4 z1z1 z3z3 z4z4 z2z2