Physics II

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Physics II

• Wave Mechanics

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Wave-particle duality for light

• Electromagnetic wave
• Describe e-m radiation as a wave of electric and
  magnetic fields propagating as a transverse wave
  in vacuo at 299792458 m/s
• Interference and diffraction effects
• Photon
• E-m radiation interacting with matter acts is if
  the energy were localized
• Photoelectric effect (Einstein)
• Compton Scattering

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A prince of a fellow

• Wave particle duality extended to matter

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From special relativity

• E2 p2c2 m2c4
• For light, the rest mass of the photon is zero
  (m0)
• Hence E pc
• E hf hc / ? pc
• p h/ ?
• ? h/p The famous DeBroglie wavelength

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How to find p

• When speeds are small compared to speed of light
• KE mv2/2 m (p/m)2 /2 p2 / (2m)
• Since p mv
• Relativistic p mv / sqrt (1 v2/c2 )
• If a charged particle undergoes a potential drop
  of qV, its kinetic energy increases by
• KE qV

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Experimental Verification

• Davisson-Germer experiment
• http//hyperphysics.phy-astr.gsu.edu/hbase/davger.
  html

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Complementarity

• Niels Bohr enunciated his principle of
  complementarity to try to reconcile the
  wave-particle duality
• He noted that the two pictures, while seemingly
  contradictory, are both in some sense true and
  must be both used to find the complete picture.
• Contraria sunt complementa
• Nur die Fülle führt zur Klarheit, Und im Abgrund
  wohnt die Wahrheit

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Formal complementarity

• For photon
• E2 (pc)2 0
• ?2 (kc)2 0
• These describe the same entityphoton
• Identify
• E hf h ?/(2?)
• p E/c hf / c h / ? h (2?/?)/(2?) hk
  /(2?)

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Formal Complementaryity 2

• For electron
• E2 (pc)2 (mc2)2
• By analogy with photon we associate frequency and
  wave number analog
• ?2 (kc)2 ?02
• DeBroglie suggested these, too, describe same
  material entity and we view matter and radiation
  in a unified way.
• E h ?/ (2?)
• p hk / (2?)

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The DeBroglie wavelength

• p hk / (2?)
• p ( h (2 ?)/?)/ (2?)
• p h / ?
• Notice this
• p ? h
• Momentum and wavelength inextricably coupled
• Therefore wave and particle nature also
  inseparable.

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Schrodinger Equation

• Principles of least action
• Fermat (optics)
• Hamiltons Equation (mechanics)
• Hamilton-Jacobi equation (mechanics)
• Schrodinger replaced variables in classical
  physics with operators in q.m.
• Incorporate non-commutability
• pq not equal to qp

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The wave function Psi

• The solution to the Schrodinger Equation, called
  Psi has interesting properties
• Scalar with time and space variation and may be
  many-dimensional
• Non-relativistic
• May be imaginary
• Hence has no physical reality in itself.
• Multiplied by its complex conjugate its (Born) a
  probability density!
• Sometimes called an orbital

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Probability

• Two uses of probability in physics
• Use vast numbers to apply statistics to hide
  ignorance of quantities that are indeed
  determined but too hard to calculate
• Gases, liquids, solids, etc.
• Represent a real, intrinsic probability in the
  inner workings of nature.
• God does not play dice with the Universe
• A. Einstein
• Wave function deterministic, experimental result
  random but depends on wave function.

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Einstein did not buy this randomness

• Gott spielt nicht Würfel mit dem Universum
• Einstein-Rosen-Podalski experiment
• John Bells reification
• Aspects results
• QM is right, naïve realism is wrong.