1. 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
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2. Group Velocity - history. See groupvelocity_Mcdonald_1996
Group Velocity - history ... See groupvelocity_Mcdonald_1996.pdf on Studentportal
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3. 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
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5. 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
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6.
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8. New version of the drawing, see also the following
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10. 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
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11. Changes to be done - noticed in the lectures REMEMBERED: DONE
Remember polar plot page
-> 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
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STILL REMEMBER:
more on matlab wavepackets;
Java wavepacket
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