The strange (and beautiful) world of Quantum Mechanics
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2 The strange (and beautiful) world of Quantum Mechanics K.L. Sebastian Department of Inorganic and Physical Chemistry Indian Institute of Science Bangalore
3 The strange (and beautiful) world of Quantum Mechanics Very frightening Just beautiful!
4 Outline 1. Wave or Particle?..Two slit experiments 2. Uncertainty Principle 3. Standing Waves 4. Stationary States - Atomic Orbitals 5. States of a Quantum System 6. Do we understand Quantum Mechanics? 7. The Path Integral Random Walk
5 With particles (bullets) Two Slit experiments
6 I 1 I I 2 Behavior of bullets is easy to understand LUMPINESS
7 With waves (water waves) I 12 I 1 I I 2
8 1 I / d i s p l a c e m e n t 2 / j à j 2 I 1 = j à 1 j 2
9 2 I 2 = j à 2 j 2
10 I I 1 2 = j à 1 2 j 2 2 à 1 2 = à 1 + à 2
11 Waves interfere! NO LUMPINESS!
12 With electrons Electrons are like bullets - lumps I 1 I 12 I I 2
13 LUMPINESS- INTERFERENCE I 1 2 / j à 1 2 j 2
14 1/1000 mm
15 American Journal of Physics, 57, 117 (1989)
16 This type of behavior was observed first in the case of light! God does not play dice!
17 Newton Light is a beam of particles History EM Theory, hence waves Exhibits interference, hence waves! Huygens Einstein In photoelectric effect, light behaves like particles Maxwell Compton In my scattering expts, light - beam of particles
18 On Mondays, Wednesdays and Fridays, it is a PARTICLE! On, Tuesdays,Thursdays and Saturdays it is a WAVE! Oh LORD, please, is it a PARTICLE or a WAVE!!??? On Sundays It is both! It has a DUAL NATURE Not only electrons and photons,but EVERYTHING has this dual nature! Exptly shown for protons, neutrons, He atoms, even C 60!
19 C 60 Prof. A. Zeilinger
20 Duality Whom do you see in this picture? A young girl? Old woman?
21 De Broglie - Heisenberg de Broglie Heisenberg
22 Reflection
23
24 Modes of a String - Standing waves
25
26
27
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29 Standing waves of a bridge
30 On a rectangular membrane Stretched membrane Time dependent wave
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32
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34 Stretched membrane No nodes One node One node Two nodes Four nodes Infinite modes
35
36 Box Standing wave patterns in 2D can be formed! Particle in a box
37 From work of Eigler (IBM)
38 From work of Eigler (IBM)
39 From work of Eigler (IBM)
40 - Box + Standing wave patterns in 3D can be formed! Hydrogen Atom: e - bound to proton
41 Atomic Orbitals p z d z 2 d xy Standing waves in 3 dimensions f z 3 g z 4
42 leads to bonding Electron density goes into internuclear region! Constructive interference! Electron density goes away from the internuclear region! Destructive interference!
43 Do we understand Quantum Mechanics?
44
45 How does it know that both the slits are open!!?? At least this time, he is sensible! I don t understand it!! Nobody does!!!
46 Does it go through both the slits?
47
48 How does an electron move (propagate)? He is crazy! Through all possible paths!
49 More slits Source of particles Even more Complex setup
50 In the limit of walls each with slits. All paths contribute! Action
51 Quantum mechanics and the drunken walker
52 Haddock in the Evening We can only talk of Probabilities! BAR
53 BAR Some paths are more probable than others
54 I have always known that the electron is weird!
55 If you have wave phenomena, then there must be a wave equation! He is crazy! Matter waves obey my equation
56 Time dependent Schrodinger Equation If you know then you can calculate My dear Calculus, Why don t stop this blabbering!??
57 Postulates The state of a system, is specified as fully as is possible, by the state function Probabililty of finding the system in a volume element is given by There he goes!
58 !!!! Corresponding to every observable of classical mechanics, there is a Hermitian operator. In order to find the operator, first write down the classical mechanical expression for the observable and then make the following replacements:
59 Every measurement of an observable leads to an eigen-value of the corresponding operator. The average of a large number of observations is given by
60 The state function obeys the time dependent Schrödinger equation That is enough!
61 The state function obeys the time dependent Schrödinger equation That is enough!
62 Special Solutions: Stationary States p z f z 3
63 ATOMIC ORBITALS
64 MOLECULAR ORBITALS
65 Electromagnetic Waves Z X l Y These too, OK
66 Spectroscopy Molecule Source of Photons GROUND STATE EXCITED!
67
68 Time dependent state of a string
69
70 Laser pulse
71 Non-standing Waves Time-dependent State of Hydrogen atom
72 REFERENCES 1. G. Gamov, Tompkins in Paperback, Canto Books. CUP, R.Gilmore, Alice in Quantum Land, Affiliated East West Press Ltd Gribbin, Schrodinger s Cat, Black Swan, London, Cropper, The Quantum Physicists, OUP, J. Gribbin, Schrodinger s Kittens, Little, Brown & Co. London, G. Gamov and R. Stannard, The New World of Tompkins, Cambridge Univ. Press, R.P. Feynamn, QED, Princeton University Press, R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw Hill, New York, 1965.
73 See: I think it is safe to say that no one understands quantum mechanics. Richard Feynman The reason universities have students is so they can teach the professors, and Feynman was one of the best (students). John Wheeler
74 Quantum Drum 30 micrometer x 20 micrometer x 500 nm Cleland et al: Nature, March, 2010.
75 What do you think of Quantum Mechanics? OR
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