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

2 Quantum theory PHOTONS energy quantized in units of ( h = Planck’s constant) momentum quantized in units of angular momentum quantized in units of blackbody radiation photoelectric effect Compton scattering PARTICLES frequency determined by energy de Broglie wavelength determined by momentum electron diffraction angular momentum quantized in units of atomic theory discrete energy levels for bound particlesatomic theory Stern-Gerlach

3 Wave-particle duality + WHAT SORT OF WAVE? transverse/longitudinal motion? + transverse density density? QUANTUM WAVEFUNCTION amplitude 2 describes probability phase has no classical analogue amplitude and phase combined to form complex number ? phase matters! rate of phase variation defines frequency and wavelength

4 Diffracting molecules S Gerlich et al, Nature Physics (2007) MOLECULE DIFFRACTION molecules behave like waves molecule wavelength molecular wavefunction

5 Ramsauer-Townsend effect S G Kukolich, Am. J. Phys (1968) A anomalous dip in scattering probability at low energy Ar proves to be interference from front and rear ‘reflections’ from Ar atom

6 Particle interference MOLECULE DIFFRACTION and RAMSAUER-TOWNSEND give particle two or more routes through experiment interference depends upon relative phases of contributions phase depends upon path difference and wavelength STATIONARY PARTICLES give particle two or more routes through experiment interference depends upon relative phases of contributions phase depends upon frequency difference and duration

7 Atomic clock energy 0 Cs atom electron density depends upon relative phase of superposition components  = GHz

8 Atomic clock x/a 0 electron density depends upon relative phase of superposition components atomic wavefunction

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

10 Quantum mechanics 1.particles behave like waves, and vice-versa 2.energies and momenta can be quantized, ie measurements yield particular results 3.all information about a particle is contained within a complex wavefunction, which determines the probabilities of experimental outcomes 4.80 years of experiments have found no inconsistency with quantum theory 5.explanation of the ‘quantum measurement problem’ – the collapse of the wavefunction upon measurement – remains an unsolved problem

11 Messenger Lecture Richard P. Feynman ( ) Nobel prize 1965 Messenger series of lectures, Cornell University, 1964 Lecture 6: ‘Probability and Uncertainty – the quantum mechanical view of nature’ The Character of Physical Law - Penguin see the later series of Douglas Robb memorial lectures (1979) online at

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

13 Single slit diffraction x amplitude intensity

14 Uncertainty HEISENBERG’S UNCERTAINTY PRINCIPLE certain pairs of parameters may not simultaneously be exactly determined {position, momentum} {time, energy} {orientation, angular momentum} {intensity, phase} {x, y}, {x, z}, {y, z} components of angular momentum {position, wavelength} {time, frequency} conjugate parameters cannot be simultaneously definite QUANTUM MEASUREMENT measurement changes observed system so that parameter measured is subsequently 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

15 Uncertainty BEATING OF TWO DIFFERENT FREQUENCIES

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