From Billiard Balls to Wave Functions, the Origin of Quantum Mechanics

Transcription

1 From Billiard Balls to Wave Functions, the Origin of Quantum Mechanics How Classical Thoughts Lead to Quantum Mechanics 1

2 History of Physics Ibn Sahl (984) discovers what we now call Snell s Law Willebrord Snellius (1621) rediscovers the same law n = index of refraction 2

3 History of Physics Observer 1629 Isaac Beeckman detonated explosives and ask observers how much time it took between seeing explosion in both mirrors. 3

4 History of Physics Path 1 Observer 1629 Isaac Beeckman detonated explosives and ask observers how much time it took between seeing explosion in both mirrors. 4

5 History of Physics Path 2 Path 1 Observer 1629 Isaac Beeckman detonated explosives and ask observers how much time it took between seeing explosion in both mirrors. His results were inconclusive 5

6 History of Physics Isaac Newton (1666) demonstrates color is an intrinsic property of light. Argue for a corpuscles model for light (light is a bunch of particles) 6

7 Formulations of Classical Mechanics - Newtonian Newtonian Mechanics (1687) - find the net force on a particle and integrate to determine the motion m 7

8 Formulations of Classical Mechanics - Hamiltonian Hamiltonian Mechanics (1833) Express the energy in phase space (q,p). Hamiltonian = Energy of system 8

9 Hamiltonian Mechanics and Action The reduced action of a system is The Hamilton-Jacobi equation We can relate the energy of a particle to the action These last two equation will be important to us later 9

10 History of Physics James Clerk Maxwell (1861) Light is a wave of combined electric and magnetic fields, called electromagnetic waves (EM wave). Changing electric and magnetic fields create a self-sustaining electromagnetic wave. 10

11 Wave front 11

12 Wave through a Single Slit What happens to a wave front when it passes through a small gap? 12

13 Wave through a Single Slit What happens to a wave front when it passes through a small gap? 13

14 Wave through a Single Slit What happens to a wave front when it passes through a small gap? This can t be right, you d never hear people unless you were directly in front of them 14

15 Wave through a Single Slit What happens to a wave front when it passes through a small gap? 15

16 Wave through a Double Slit Interference Pattern 16

17 Constructive and Destructive Interference Constructive Two waves are in phase and the resulting wave is the sum of the two Destructive Two waves are out of phase and the resulting wave is the difference of the two 17

18 Wave through a Double Slit 18

19 Particle Action Back to particles: Consider the action, S, of several particles and connect them 19

20 Classical Scattering Back to particles: Consider the action, S, of several particles and connect them Surface of constant action 20

21 Classical Scattering Back to particles: Consider the action, S, of several particles and connect them Surface of constant action 21

22 Classical Scattering Back to particles: Consider the action, S, of several particles and connect them We ve created a classical wave front! We can connect billiard balls (particles) to waves Surface of constant action 22

23 Paths of Least quantities (Optomechanical Analogy) Light Particle Fermat s Principle of Least Time Maupertuis Principle of Least Action Light takes the path from q0 to q1 that takes the least amount of time Particles takes the path from q0 to q1 of least action 23

24 The electron J.J. Thompson (1896) Using a Cathode Ray Tube discovers the electron Millikan Oil Drop Experiment (1909) measures the electron charge and discovers it is quantize. ee- e- Oil drop with 3 electrons on it 24

25 Electron through a Double Slit Detecto r Scree n Electron through a double slit 25

26 Electron through a Double Slit Detecto r Scree n Electron through a double slit 26

27 Electron through a Double Slit Detecto r Scree n Electron through a double slit 27

28 Electron through a Double Slit Detecto r Scree n Electron through a double slit 28

29 Electron through a Double Slit Detecto r Scree n Electron through a double slit 29

30 Electron through a Double Slit Detecto r Scree n Electron through a double slit 30

31 Electron through a Double Slit Detecto r Scree n Electron through a double slit Electron is a particle, but acts like a wave! 31

32 Electron through a Double Slit De Broglie (1924) suggested that electrons have wave properties, for instance a wavelength Wave-Particle duality! 32

33 Conclusion Physicist were trying to connect wave equations and particle motion long before the notion of quantum mechanics existed Quantum mechanics is a natural extension of the classical mechanics we are familiar with We can approximate quantum wave functions by quantizing the action of a related classical system 33