Exploring Quantum Physics – Week 1 Lecture 1
- 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
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:
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: