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Unformatted text preview: Brief Review of Quantum Mechanics • Waveparticle duality chroedinger equation for free particles in a periodic lattice • Schroedinger equation for free particles, in a periodic lattice • Effective masses • andstructure examples Bandstructure examples EEE537 Fall 2010 ECEE ASU C.Z. Ning 1 Unification of Matter and Wave • Matter particles are described by energy, E , and momentum, p • Waves are described by quantities such as k , v , λ • Einstein already assumed (as did Planck): • It was de Broglie who made another decisive assumption: ω ν h = = h E • We can associate each wave with energy and momentum k h c h p h = = = λ ν • Similarly we can associate each particle with frequency and avelength through: ω ν h = = h E k h c h p h = = = λ ν wavelength through: mE h p h 2 = = λ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = m p mv E 2 2 1 2 2 p h c = ν EEE537 Fall 2010 ECEE ASU C.Z. Ning 2 Now: particles have wave properties, and waves have particle properties Examples of Wavelength of Matter Waves Example 1: wavelength of a bullet of mass 20 g at speed of 1000 m/s: s 34 27 − m s m kg Js mv h 33 10 314 . 3 ) / ( 1000 ) ( 02 . 10 627 . 6 − × = × × = = λ There is probably nothing in the world that could detect or sense such short wavelength. Therefore Newton mechanics is fine!...
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 Fall '10
 CZNing
 ASU C.Z. Ning, ECEE ASU C.Z.

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