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Waves, Light & Quanta

Waves, Light & Quanta. Tim Freegarde. Web Gallery of Art; National Gallery, London. Quantum mechanics. particles behave like waves , and vice-versa. energies and momenta can be quantized , ie measurements yield particular results.

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Waves, Light & Quanta

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  1. Waves, Light & Quanta Tim Freegarde Web Gallery of Art; National Gallery, London

  2. Quantum mechanics • particles behave like waves, and vice-versa • energies and momenta can be quantized, ie measurements yield particular results • all information about a particle is contained within a complex wavefunction, which determines the probabilities of experimental outcomes • deterministic evolution of the wavefunction is determined by a differential (e.g. Schrödinger) wave equation • 80 years of experiments have found no inconsistency with quantum theory • explanation of the ‘quantum measurement problem’ – the collapse of the wavefunction upon measurement – remains an unsolved problem • non-deterministic process • Heisenberg’s uncertainty principle 2

  3. Quantum measurement energy • allowed energies 0 n = 3 n = 2 n = 1 THE HYDROGEN ATOM n =  QUANTUM MEASUREMENT • measured energy must be one of allowed values • …but until measurement, any energy possible • after measurement, subsequent measurements will give same value 3

  4. The experiment with the two holes    y x • fringe maxima when  fringe spacing  illumination wavelength  illumination momentum • equivalent to change in illumination angle and hence by • smallest visible feature size  4

  5. Single slit diffraction  amplitude x intensity 5

  6. Uncertainty HEISENBERG’S UNCERTAINTY PRINCIPLE • certain pairs of parameters may not simultaneously be exactly determined • {position, momentum} • {position, wavelength} • {time, energy} • {time, frequency} • {orientation, angular momentum} • {linear, circular} polarization • {intensity, phase} • {x, y}, {x, z}, {y, z} components of angular momentum • conjugate parameters cannot be simultaneously definite 6

  7. Uncertainty BEATING OF TWO DIFFERENT FREQUENCIES 7

  8. Bandwidth theorem 8

  9. Bandwidth theorem 9

  10. Bandwidth theorem 10

  11. Terminology • expectation value = mean • uncertainty = standard deviation • probability of given result given by UNCERTAINTY IN MEASUREMENT • repeated experiment yields range of results • before measurement, system was in a superposition 11

  12. Uncertainty HEISENBERG’S UNCERTAINTY PRINCIPLE • certain pairs of parameters may not simultaneously be exactly determined • {position, momentum} • {position, wavelength} • {time, energy} • {time, frequency} • {orientation, angular momentum} • {linear, circular} polarization • {intensity, phase} • {x, y}, {x, z}, {y, z} components of angular momentum QUANTUM MEASUREMENT • measurement changes observed system so that parameter measured is subsequently definite • conjugate parameters cannot be simultaneously definite • process measure A, measure B not the same as measure B, measure A • measure A, measure B are not commutative / do not commute • commutator [measure A, measure B]  0 12

  13. The LASER LIGHT AMPLIFICATION by Stimulated Emission of Radiation • Theodore Maiman, 16 May 1960 mirror beam splitter 693.4 nm ruby flash tube light amplifier optical resonator 13

  14. Absorption and emission of photons SPONTANEOUS EMISSION energy 0 n = 3 n = 2 STIMULATED EMISSION n = 1 ABSORPTION n =  ABSORPTION absorption emission 14

  15. Absorption and emission of photons SPONTANEOUS EMISSION • thermal equilibrium STIMULATED  blackbody spectrum EMISSION • amplification of light if atomic population is inverted i.e. ABSORPTION EINSTEIN EQUATIONS • Einstein A and B coefficients ABSORPTION • spontaneous emission stimulated by vacuum field 15

  16. The ruby LASER energy mirror beam splitter 693.4 nm ruby flash tube metastable light amplifier optical resonator • Cr3+ ions in sapphire (Al2O3) absorb blue and green from flash light absorption emission • internal transitions to metastable state Cr3+ • spontaneous emission is amplified by passage through ruby • repeatedly reflected/amplified near-axial light builds up to form coherent laser beam 16

  17. Laser beam characteristics mirror beam splitter ruby flash tube • narrow linewidth for long pulses ( ) 693.4 nm • as initial source recedes down unfolded cavity, emission approaches that from distant point source • divergence determined by diffraction by limiting aperture • focusable • constructive interference between reflections for certain wavelengths • long pulse  continuous wave (c.w.) • monochromatic • noise from spontaneous emission gives lower limit to linewidth • nonlinear processes have various effects in detail • Hecht section 13.1 17

  18. The ruby LASER mirror beam splitter 693.4 nm ruby flash tube light amplifier • ray optics • colour optical resonator • diffraction • interference • quantum physics • refraction, polarization, … 18

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