Lecture Wednesday 26. March 2008 Lecture Thursday 27. March 2008 Topics: Effective mass – transport in periodic structures Bloch state properties Associated texts: EffectiveMass2008_SLIDES.pdf groupvelocity_Mcdonald_1996.pdf on Studentportal Group velocity Expectation value of momentum <p> -> assign velocity as <p>/m Quantum mechanics and forces ? Constant force -> inclined plane potential (linear function) Wave packet; Transport Model Bloch E = a – b cos (ka) -> understanding of effective mass Comment: Edited April 1st,2008 PHYS208 26. and 27.03.2008 page 1

Group Velocity - history. See groupvelocity_Mcdonald_1996 Group Velocity - history ... See groupvelocity_Mcdonald_1996.pdf on Studentportal PHYS208 26. and 27.03.2008 page 2

Deriving the Schrödinger-like equation for the periodic function u(r) To derive the expectation value of momentum p, we differentiate the whole Schrödinger-like equation for u(r) with respect to k PHYS208 26. and 27.03.2008 page 3

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Correspond to pulses in light and radiowaves Narrow in MOMENTUM broad in MOMENTUM Broad in SPACE narrow in SPACE Wave packets; Special types of superposition solutions; Explain the classical Transport in quantal terms; Correspond to pulses in light and radiowaves PHYS208 26. and 27.03.2008 page 5

http://web.ift.uib.no/AMOS/MOV/WAVE/ PHYS208 26. and 27.03.2008 page 6

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New version of the drawing, see also the following PHYS208 26. and 27.03.2008 page 8

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The key is the velocity graph as k increases, the position in band «increases», i.e. the energy in band increases But the velocity in that region DECREASES Thus NEGATIVE MASS INFINITE MASS: The velocity does not change (or only very little) close to its maximum or minimum If push does not change velocity – mass is very large, even infinite PHYS208 26. and 27.03.2008 page 10

Changes to be done - noticed in the lectures REMEMBERED: DONE Remember polar plot page http://web.ift.uib.no/AMOS/PHYS261/2007/POLAR/ -> Group velocity files – add our to our text – done – 2008 version -> say that momentum is calculated - edited -> McDonald to Studentportal Wavepackets in matlab PAK98 directory i-index effective mass (misprint; corrected) missing square paranthesis in group velocity ____________________________________________ STILL REMEMBER: more on matlab wavepackets; Java wavepacket PHYS208 26. and 27.03.2008 page 11