Institute of Solid State Physics

Molecular and Solid State Physics

Technische Universität Graz

Peter Hadley

Calculate the macroscopic properties from the microscopic structure.

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.

513.001 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

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

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

Wave functions of hydrogen

2 22

02 4e E

m r

Solve with the boundary condition 0 as r

Assume ( , , ) ( ) ( ) ( )r R r

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

Hydrogen wavefunctions

quantum numbers n,l,m

l = 0...n-1

m = -l ...0...l

l = 0 sl = 1 pl = 2 dl = 3 f