1. Quantum physics Quantum physics can be traced to a single concept: Each particle is associated with a wave and vice versa. These are two different aspects of the same object. For example, an electromagnetic wave is associated with a particle, the photon. The puzzle will be resolved by introducing the concept of a wave packet (called wave function in physics): The wave packet determines the probability of finding the particle. Ch. 12

2. The wave packet determines the probability of finding the particle. Number of of a light wave = Probability of finding a photon Buildup of a diffraction pattern from individual photons. Probability in quantum physics

3. Consequences of the particle/wave concept 1) The Quantum –The energy of a wave takes discrete values (quanta), because a wave consists of discrete particles. –For example, a laser beam consists of many photons, each carrying the same photon energy. 2) Probabilities –One cannot predict exactly how an individual particle will behave. The probability can be obtained from the intensity of the wave packet. –Accurate results can be obtained after repeating the same experiment with many particles and averaging.

4. 3) The Uncertainty Relation –There is a tradeoff between particle and wave character. –Depending on the width of the wave packet, an object can be more like a particle or like a wave. –A particle (short wave packet) has a well-defined position, and a wave ( long packet) has a well-defined momentum. –That leads to a tradeoff between the uncertainties in the position and the momentum. These results will be fleshed out in the following lectures.

5. Fortunately, the strange rules of quantum physics affect only very small objects, such as individual atoms and electrons. As soon as we have a macroscopic object consisting of many atoms, an experiment becomes more predictable. Typically, a macroscopic object consists of 10 24 atoms (Avogadro’s number). Averaging over 10 24 atoms reduces the statistical error to 1/  10 24 = 1/10 12 = 1 in a trillion.

6. Relativity makes the result of a measurement dependent on the observer. Quantum physics goes farther and makes a measurement on a single particle uncertain.

7. Special relativity: Important for high velocities General relativity: Important for strong gravity Quantum physics: Important for small objects

8. Planck found that the radiation from a glowing object can be explained only by assuming that energy is radiated in discrete quanta. The size of an energy quantum is: Origins of quantum physics E = Energy of a particle f = Frequency of a wave h = Planck’s constant ħ = E = h · f h 2 

9. Einstein explained emission of electrons from a solid by light in 1905, using the concept of light particles = photons. The energy of a photon is: Nothing happens if the energy of the photons is too low (red light). He later received his Nobel prize for this work (not for relativity!). E = h · f Waves as Particles

10. Particles as Waves 54 eV electrons = 0.17 nm DeBroglie predicted that particles should behave like waves. Davisson and Germer observed that electrons are diffracted by a nickel crystal. This is analogous to the diffraction of light waves (Lecture 9). Bright spots: Interference pattern

11. Generalization: Every particle is a wave, and vice versa Particle properties: Energy E Momentum p E = h / T Wave properties: Period in time = T = 1/f Period in space = p = h / (Compare waves, Lect. 8, Slide 4) (Planck) (de Broglie)

12. Equations for waves Electron waves are described by the Schrödinger equation. (Erwin Schrödinger 1926) Its relativistic generalization is the Dirac equation. (Paul Dirac 1928)

13. Photon waves (electromagnetic waves) are described by Maxwell’s equations. Although Maxwell’s equations appeared decades before relativity and quantum physics, they are perfectly compatible with these new theories. That is one more reason why physicists are fond of them. Mathematical elegance proved to be a good criterion for correct physics. The equations of general relativity are also very elegant, but incompatible with quantum theory. String theorists have quite elegant equations for quantum gravity, but these are not testable.