Interactions of Electromagnetic Radiation Photons of elm wave arrive at antenna and induce synchronized electric current Electromagnetic wave guiding (?) photons Int Elm Rad Receiver Radio Tower W. Udo Schröder, 20018

Interactions with Electric and Magnetic Fields Since 1900’s: (Maxwell) classical unified theory of continuous elm fields describing most macroscopic observations. Features incompatible with classical picture: Planck’s radiation laws  elm energy is granular (“quantized”) Photoelectric/Compton effects  photons are corpuscular field quanta (mass-less bosons), spatial correlations with fields but straight trajectories Macroscopic absorption/emission patterns for elm radiation have superimposed/embedded fine structure, threshold behavior (heat capacity) Characteristic material dependence of absorption/emission  discrete internal structure of microscopic systems (molecules, atoms, nuclei,..) Important spectroscopic tool Int Elm Rad Task: Develop quantitative quantal theory of elm interactions with matter Method: 1. Review classical electric and magnetic interactions with charged particles 2. Derive interaction Hamiltonians and associated wave functions/vectors 3. Use Correspondence Principle to quantize classical elm multipolar fields , characterize field quanta 4. Apply to spectroscopy W. Udo Schröder, 20018

Continuous & Discrete Electromagnetic Spectra Spectrum = Intensity vs. color (wave length). (Intensity = number of photons.) Bound charges (electrons in atoms or molecules, ions or protons in nuclei) emit and absorb electromagnetic waves (photons) with discrete (characteristic) energies. Free moving charges emit a Maxwell-Boltzmann type elm. spectrum reflecting spectrum of particle velocities. Blackbody Sun Looking at Sun through gas l  molecules Spectrometer l  l  Looking directly at gas Looking directly at Sun

Characteristic Emission and Absorption Spectra Sun Unbound (free) electric charges such as electrons in a macroscopic, hot mass (“blackbody”) of ionized gas (e.g., Sun) emit and absorb electromagnetic spectra with continuous wavelengths (frequencies, photon energies). Bound (spatially confined) electric charges (e.g., electrons in atoms, molecules) emit and absorb discrete (“line”) energy (wavelength) spectra. Ionization Energy Energy transfer by photons in bound systems: Absorption or emission of light quanta occurs in (reversible) transitions between discrete energy levels. Characteristic spacing  spectr. ID Also: Excitation in chemical rxns. DE DE -DE Ground State |DE| = hn = hc/l h = 6.62606957 × 10-34 m2 kg / s Planck’s constant

Characteristic Emission And Absorption Spectra Reversible transitions between discrete energy levels Sun Ionization Energy Unbound electric charges such as electrons in a hot body (“blackbody”) of ionized gas (e.g., Sun) emit and absorb electromagnetic spectra with continuous wavelengths (frequencies, photon energies). Bound electric charges (e.g., electrons in atoms, molecules) emit and absorb discrete (“line”) energy (wavelength) spectra. DE Energy transfer by photons in bound systems: Absorption or emission of light occurs in transitions between discrete energy levels. Characteristic spacing  spectr. ID Also: Excitation in chemical rxns. DE Ground State Ground State -DE Characteristic Characteristic |DE| = hn = hc/l h = 6.62606957 × 10-34 m2 kg / s Planck’s constant

Electric and Magnetic Fields Example: RF power driven electric or magnetic dipoles broadcast t-dependent fields. AND: Irradiation of properly designed antennas with fields induce RF power in the antennas. Task: Devise quantitative microscopic theory to describe/predict spontaneous and induced elm transitions between states of molecular, atomic, nuclear,.. systems coupled to elm field. Field character can be essentially electric or essentially magnetic. (Both components are always present in t-dependent fields.) Int Elm Rad W. Udo Schröder, 20018

Electric and Magnetic Fields Strategy Recall classical electric/magnetic multipoles 2ℓ Quantize classical elm field for oscillating electric or magnetic 2ℓ poles (ℓ=1 dipole, ℓ=2 quadrupole, ℓ=3 octupole,….  Quantum wave function (non-rel.) Derive interaction Hamiltonian  Use perturbation theory to calculate rates for transitions between unperturbed system states. 2nd quantization of elm fields in terms of field quanta Int Elm Rad W. Udo Schröder, 20018

Symmetry Concept: Multipolar Electric and Magnetic Fields Electric multipole moment Magnetic multipole moment Partial integration  El. multipole moment unit = e×(length)ℓ , magn. multipole moment unit = µB×(length)ℓ−1, e = elementary charge, µB = Bohr magneton. ∇ · B = 0  there are no magn. monopoles. Concept of magn. monopole useful in describing magn. features of composite objects Int Elm Rad Useful representation of spherical harmonics: zero or positive integers p, q, and s, with p + q + s = ℓ and p − q = m. W. Udo Schröder, 20018

Parity: A Quantal Symmetry For spatially symmetric charge distribution Hamiltonian is invariant against space inversion y x x n even  p = +1 n odd  p = -1 Int Elm Rad For “good” parity no permanent odd el moment W. Udo Schröder, 20018