Institute of Solid State Physics
Molecular and Solid State Physics
Technische Universität Graz
Peter Hadley
Calculate the macroscopic properties from the microscopic structure.
PHYF20 Molecular and Solid State Physics
At the end of this course you should be able to explain how any property of any molecule or solid can be calculated using quantum mechanics and statistical physics.
For example: knowing how the atoms are arranged in a crystal, you must be able to say if it is an electrical conductor or not.
Goals
The microscopic structure determines the macroscopic properties.
PHYF20 Molecular and Solid State Physics
There are billions of useful molecules.
Acids, esthers, alkanes, ...Biological molecules: DNA, RNA, proteins
Molecules
Molecular and Solid State Physics
Every property of a molecule can be calculated using multi-particle quantum mechanics.
Molecules
We will calculate:bond lengthbond strengthmolecular energy levels
http://en.wikipedia.org/wiki/File:Erwin_Schr%C3%B6dinger.jpg
Molecules
We will calculate:bond lengthbond strengthmolecular energy levels
PHYF20 Molecular and Solid State Physics
Solids are large molecules
Solids
Crystal structuresDetermining crystal structures with x-ray diffraction Photons in solidsPhonons in solids (lattice vibrations)Thermal propertiesFree electron modelBand structure (metals, semiconductors, insulators)Semiconductors
glass
Insulin crystalsGallium crystals quartz
Crystal = periodic arrangement of atoms
amorphous siliconamorphous metal
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Institute of Solid State Physics
Books Technische Universität Graz
e-book
e-book
e-book
e-booke-book
http://www.if.tugraz.at/ss1.html
http://www.if.tugraz.at/ss1.html
Student Projects
Do something that will help other students
Review of atomic physics
Estimating the size of an atomThe hydrogen atomThe helium atomMany electron atoms
Estimate the size of a hydrogen atom
Potential energy2
0
( )4
eU rr
Uncertainty relation 2xx p
For an atom: x ~ r0
02xpr
Ur
Estimate the size of a hydrogen atom
22x x xp p p 0xp
Kinetic energy in x-direction =
2 2
202 8
xkin
pE
m mr
2
2 2
02x xp pr
2 2
2 2kinmv pE
m
02xpr
Confinement energy
Kinetic energy in x-direction =
Confinement energy:
2 2 2 2
20
32 2 2 8
x y zp p pm m m mr
E
r0
2 2
202 8
xkin
pE
m mr
Estimate the size of a hydrogen atom
Total energy = Kinetic + Potential
2 2
20
38 4tot
eEmr r
2 2
3 20
34 4
totdE edr mr r
2110
0 2
3 4.0 10 mrme
110 5.3 10 ma
Confinement energy
2 22
02 4e E
m r
2 p mv p k k
2 2 2 221
2 22 2 2kinp k hE mvm m m
The kinetic energy term increases as the wavelength gets smaller