3.012 Fund of Mat Sci: Bonding Lecture 1 bis. Photo courtesy of Malene Thyssen,

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1 3.012 Fund of Ma Sci: Bonding Lecue 1 bis WAVE MECHANICS Phoo couesy of Malene Thyssen, Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

2 Las Time 1. Playes: paicles (poons and neuons in he nuclei, elecons) and elecomagneic fields (phoons) 2. Foces: elecomagneic 3. Dynamics: Newon (macoscopic), Maxwell (fields), Schödinge (micoscopic) 4. De Boglie elaion λ p = h Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

3 Homewok fo Mon 12 You know by now: 12.5, 13.2, 13.3 Sudy: 13.4 and 13.5 Noes on hamonic oscillao -- Secion 14.1in Moime, R. G. Physical Chemisy. 2nd ed. San Diego, CA: Elsevie, Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

4 Hamonic Oscillao (I) Saionay objec Sping Mass z Equilibium posiion of mass 0 z A mass on a sping. This sysem can be epesened by a hamonic oscillao. Figue by MIT OCW Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

5 Hamonic Oscillao (II) Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

6 Hamonic Oscillao (III) Gaph of he behavio of a hamonic oscillao emoved fo copyigh easons. See Moime, R. G. Physical Chemisy. 2nd ed. San Diego, CA: Elsevie, 2000, p. 495, Figue Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

7 The oal enegy of he sysem Kineic enegy K Poenial enegy V Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

8 Pola Repesenaion Diagam of he Agand plane emoved fo copyigh easons. See Moime, R. G. Physical Chemisy. 2nd ed. San Diego, CA: Elsevie, 2000, p. 1011, figue B Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

9 A Taveling Plane Wave Ψ (, ) = Aexp[ ik ( ω)] Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

10 Pinciple of Linea Supeposiion Phoo couesy of Spialz Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

11 Wave-paicle Dualiy Waves have paicle-like popeies: Phooelecic effec: quana (phoons) ae exchanged disceely Enegy specum of an incandescen body looks like a gas of vey ho paicles Diagams of he phooelecic effec and of a P-N sola cell, emoved fo copyigh easons Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

12 Wave-paicle Dualiy Paicles have wave-like popeies: Elecons in an aom ac like sanding waves (hamonics) in an ogan pipe Elecons beams can be diffaced, and we can see he finges (Davisson and Geme, a Bell Labs in 1926 ) Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

13 When is a paicle like a wave? Wavelengh momenum = Planck Image of he double-sli expeimen emoved fo copyigh easons. See he simulaion a hp:// "Samples fom Visual Quanum Mechanics": "Double-sli Expeimen." λ p = h ( h = x J s = 2π a.u.) See animaion a hp:// Selec Samples fom Visual Quanum Mechanics > Double-sli expeimen Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

14 3.012 Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005) Time-dependen Schödinge s equaion (Newon s 2 nd law fo quanum objecs) i V m Ψ = Ψ + Ψ ), ( ), ( ), ( ), ( h h 1925-onwads: E. Schödinge (wave equaion), W. Heisenbeg (maix fomulaion), P.A.M. Diac (elaivisic)

15 Plane waves as fee paicles Ou fee paicle wave equaion: h 2m Ψ(, ) Ψ(, ) = Aexp[ i( k ω)] = ih Ψ(, ) 2 2 saisfies he p h k (povided E = h ω = = ) 2m 2m Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

16 3.012 Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005) Saionay Schödinge s Equaion (I) i V m Ψ = Ψ + Ψ ), ( ), ( ), ( ), ( h h *

17 Saionay Schödinge s Equaion (II) h 2 2m 2 + V ( ) ϕ ( ) = E ϕ ( ) Fundamenals of Maeials Science: Bonding - Nicola Mazai (MIT, Fall 2005)

3.012 Fund of Mat Sci: Bonding Lecture 11. The future of electronics? A pentacene molecule deposited on SiO 2. Image removed for copyright reasons.

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