1. Wave Physics
PHYS 2023
Tim Freegarde

2. Wave Physics WAVE EQUATIONS & SINUSOIDAL SOLUTIONS
general wave phenomena
wave equations, derivations and solution
sinusoidal wave motions
complex wave functions
WAVE PROPAGATION
Huygens’ model of wave propagation
interference
Fraunhofer diffraction
longitudinal waves
BEHAVIOUR AT INTERFACES
continuity conditions
boundary conditions
SUPERPOSITIONS
linearity and superpositions
Fourier series and transforms
FURTHER TOPICS
waves in three dimensions
waves from moving sources
operators for waves and oscillations
further phenomena and implications

3. Amplitude and power spectra
amplitude spectrum
power/intensity spectrum
Square wave

4. Discrete Fourier transform
PERIODIC WAVEFUNCTION
DISCRETE SPECTRUM
COMPLEX SPECTRUM
COMPLEX WAVEFUNCTION

5. Continuous Fourier transform
PERIODIC WAVEFUNCTION
DISCRETE SPECTRUM
NON-PERIODIC WAVEFUNCTION
COMPLEX WAVEFUNCTION & SPECTRUM

6. Fourier transforms Any waveform may be expressed as...
a function of time [position]...
...or...
a function of frequency [wavenumber]
...where most physical examples are the real part
For a single or isolated frequency component,
Dirac δ-function

7. Fourier transform variations*
terminology:
transform
analysis
synthesis
function periodicity:
discrete transform
continuous transform
integration limits:
scale factors:
reference functions:
signs:
* no correlations between rows – ie transform doesn’t mean scale factor = 1 etc.

8. Operators for wave motions
indicated by ‘hat’
can apply to continuous variables
can depend upon derivatives
recipes for determining ‘observables’
...but normalized:
...and brackets omitted:
hence operator equation

9. Operators for wave motions
QUANTUM MECHANICS
CIRCUIT THEORY
inductor
total energy
capacitor
momentum
Schrödinger’s equation
with complex impedances:

10. Operators for wave motions
Gaussian wave packet
expectation value = weighted mean

11. Wave Physics
for handouts, links and other material, see