1. Elm Field Quanta: Nature of Photons
Are massless (mg = 0) and have no charge
Have linear momentum
Travel in straight line trajectories, velocity = c
Scatter off charged particles (“elm interaction”) and other photons
Have helicity h= ±1 (like intrinsic spin Sg =1 ) directed
Photo effect: Momentum Transfer
Momentum Transfer
Linear polarization
Recoil
Helicity Transfer
Int Elm Rad Photons
Torque
Circular polarization
W. Udo Schröder, 2018

2. Elm Field Quanta: Nature of Photons
Photons are relativistic, have no mass (mg = 0) and no charge (qg = 0);
Have linear momentum , helicity h= ±1 = intrinsic spin (Sg =1) directed ;
Travel in straight-line trajectories, constant velocity = c;
Scatter off charged particles and other photons, are absorbed or emitted by charged particles (“electro-weak interaction”);
Carry angular momentum, in addition to intrinsic spin.
Photo effect: Momentum Transfer
Momentum Transfer
Linear polarization
Recoil
Helicity Transfer
Int Elm Rad Photons
Torque
Circular polarization
Conversion linearcircular polarization
W. Udo Schröder, 2018

3. Scalar or Pseudo-Scalar Interaction
Interaction of charged system with elm field is of the j·A type,
Mirror
Polar
Axial
Transformation Properties Polar vs. Axial Vectors
Vector product of 2 polar vectors is a scalar. Product of axial vector with polar vector is pseudo-scalar, behaving differently under reflexion (parity) transformation. Axial vectors:
Int Elm Rad Photons
Interaction connects system states of different properties, depending on vector nature of Aphoton, linear or circular photon polarization, multipolar angular momentum transfer.
Construct ℓ–specific and polarization-specific photon fields=wave function of ensemble of photons.
W. Udo Schröder, 2018

4. Photon Helicity/Spin x z y
Photons as relativistic m=0 particles must have intrinsic helicity h, exactly || to propagation  otherwise similar to spin
Rotating vector field (magnitude + direction)
Int Elm Rad Photons
W. Udo Schröder, 2018

5. Circular Polarization Photonsx y z
Rotating vector field (magnitude + direction)
Int Elm Rad Photons
W. Udo Schröder, 2018

6. General Structure: Circular Polarized Photonsx y z
Vector field rotating about z (=k) axis, 2 components
Rotating vector field (magnitude + direction)
Helicity has to be accounted for in angular-momentum balance, like regular spin. Photons of multipolarity ℓ transfer total angular momentum
Int Elm Rad Photons
Above solution= circular wave, contains all orbital angular momenta ℓ. But only m=0 projections onto propagation direction . For spectroscopy need solutions with specific total angular momenta .  Construct specific photon wf .
W. Udo Schröder, 2018

7. Energy and Photon Number Density
Normalize classical energy density of oscillating elm field to qu. photon numbers, assuming no quantum-statistical restrictions:
Int Elm Rad Photons
W. Udo Schröder, 2018

8. Photons as Elm Field Quanta: 2nd Quantization
Int Elm Rad Photons
W. Udo Schröder, 2018

9. Int Elm Rad Photons
W. Udo Schröder, 2018

10. Multipolar Photon Absorption/Emission
Int Elm Rad Photons
W. Udo Schröder, 2018

11. Photon State Density fℓm r R0
Auxiliary construction: Consider radial part of #spherical waves fℓm that fit into spherical cavity of radius R0. Conducting cavity shell  boundary condition fℓm(R0)=0. Result is independent of R0. Finally let R0 ∞. r
fℓm R0
Int Elm Rad Photons
W. Udo Schröder, 2018

12. Int Elm Rad Photons
W. Udo Schröder, 2018

13. The Photoelectric Effect (Discovery of Photons)Vg
collector
emitter
grid
Ammeter e-
variable voltage
Color selector (slit)
strong arc lamp + - -+
color analyzer
current A
High Light Intensity
Low Light Intensity
grid voltage Vg
V(n1)
V(n2)
aperture
retarding voltage Vg
Illuminated metal plate emits electrons with a fixed energy K(n)= eV(n) >0
and momentum p = ✔2mK. K is independent of light intensity, but depends on color (n) of light. measured if K >-V
Einstein: transfer of light-energy packet (photon) E=hn to bound electron
K = hn-hn0 work function hn0
Photons have momentum, like particles!