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

Photoelectric Effect Classical predictions fail to account for experimental observations slope=b=h

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

Diffraction

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

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

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

The Schrödinger Equation Consider the space p dependent 1st Harmonic Recall

The Schrödinger Equation Eigen Relationship

The Time Dependent Schrödinger Equation Consider the time dependent part

The Time Dependent Schrödinger Equation Propagates the wave function through time

The Time Dependent Schrödinger Equation wt ro wo Re Im Norm is preserved over time

Propagators

Propagators Unitary Transformation

Summary

Quantum Mechanics for Many Particles z1 z3 m4 m2 z4 z2 (0,0,0)