*Exploring Quantum Physics – Week 1 Lecture 1*

## Early Experiments

**Photo electric effect**: beam of light hitting charged plates with a potential across them creates current.*Expected*: amount of current is independent of frequency of the light, dependent on the intensity.*Actual*: current depends on frequency of light (no current below frequency threshold), independent of intensity.- Einstein proposed photons (nobel prize)

**Electron diffraction**: (Davisson-Germer experiment)- Crystalline structure acts as a diffraction grating, electron beam demonstrates wave interference like light.
- Experiment supports DeBroglie hypothesis:

, - For a derivation of the DeBroglie wave length, see

http://www.chip-architect.com/physics/deBroglie.pdf

## Wave Equation

Wave equation:

*Where k is the wave number*

*Where c is the wave velocity*

We can represent particles as a wave (but not the other way around) via the **Fourier transform**:

*Where is the “fourier harmonics” (amplitudes)*

Represent a particle as a Gaussian wave with a sharp peak:

## The Schrödinger wave equation

*Where is the wave function, and is the constant of proportionality, ignore for now.*

Since and , can write as:

Taking the derivative:

(or for a momentum vector: )

For a free particle (not in a potential field), , so:

Giving the **free schrödinger equation**:

Using the Hamiltonian for energy gives the **fundamental equation of quantum physics**:

## Particle delocalization

Take a Gaussian wave-packet

Solve schrödinger with this gives

*where delocalization time*

Recognize the **Gaussian integral**:

Gives wave-function in momentum space:

Notice the uncertainty , but . This is a manifestation of the **Heisenberg uncertainty principle**: