molecular and solid state physics - tu graz
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Institute of Solid State Physics
Molecular and Solid State Physics
Technische Universität Graz
Peter Hadley
Calculate the macroscopic properties from the microscopic structure.
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513.001 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.
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513.001 Molecular and Solid State Physics
There are billions of useful molecules.
Acids, esthers, alkanes, ...Biological molecules: DNA, RNA, proteins
Molecules
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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
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Molecules
We will calculate:bond lengthbond strengthmolecular energy levels
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513.001 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
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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
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http://www.if.tugraz.at/ss1.html
http://www.if.tugraz.at/ss1.html
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Student Projects
Do something that will help other students
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Review of atomic physics
Estimating the size of an atomThe hydrogen atomThe helium atomMany electron atoms
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Estimate the size of a hydrogen atom
Potential energy2
0
( )4
eU rr
Uncertainty relation 2xx p
For an atom: x ~ r0
02xpr
Ur
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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
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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
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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
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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
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Wave functions of hydrogen
2 22
02 4e E
m r
Solve with the boundary condition 0 as r
Assume ( , , ) ( ) ( ) ( )r R r
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Hydrogen atom
0
2 rna
2 11 ( )l
n lL
( , )lmY
a0 = Bohr radius
= generalized Laguerre polynomials
= spherical harmonics (appear in centrosymmetric problems)
2 22
02 4e E
m r
3/ 2 2 1
10
1 !2, , ,2 !
l ln lm n l lm
n lr e L Y
na n n l
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Hydrogen wavefunctions
quantum numbers n,l,m
l = 0...n-1
m = -l ...0...l
l = 0 sl = 1 pl = 2 dl = 3 f