PHYSICAL CHEMISTRY ADVANCED MATERIALS

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PHYSICAL CHEMISTRY - ADVANCED MATERIALS
LECTURES Dr. Elizabeth Santos Tel. (0731)
50-31342Fax [phone] O25-344Email
esantos_at_uni-ulm.de http//www.pctheory.uni-ulm.de/
Albert-Einstein-Allee 11D-89069 Ulm
EXERCISES Germán Soldano Room. O25/343 Tel.
49 731 50 31344 E-Mail german.soldano_at_uni-ulm.de
EXERCISES Xin QiEmail xin.qi_at_uni-ulm.de
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PHYSICAL CHEMISTRY - ADVANCED MATERIALS PROGRAM
Quantum Mechanics Introduction of Fundamental
concepts
Classical Waves Some Fundamental Concepts about
Waves Simple Harmonic Motion Wave Motion
The Classical Wave Equation Wave function
Concepts of Eigenfunction and Eigenvalue
Conditions Standing and Travelling Waves The
Complex Representation of Waves Light as an
Electromagnetic Wave Waves Phenomena
Reflexion, Refraction, Interference and
Diffraction Principle of Superposition
Fourier Series Separation of Variables. Particl
es and Waves Experiments contradicting the
classical approximation Black-Body Radiation,
Photoelectric Effect, Electron Diffraction The
Wave Nature of Matter Waves and the Uncertainty
Principle The Work of Bohr on Atomic Spectra
Some Insight into the Schrödinger Equation
Interpretation of the Wave Function in Quantum
Mechanics Postulates of Quantum Mechanics
Brief Introduction on Operators Hamiltonian and
Eigenvalues.
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Quantum Mechanics of Some Simple Systems The Free
Particle Particle in Box Penetration of a
Potential Barrier Application on Scanning
Tunneling Microscopy Harmonic Oscillator
comparison between classical and quantum
approaches. Quantum Mechanics Atomic Structure
and Molecules The Hydrogen Atom Wave Functions
and Orbitals Atomic Energy Levels Simple
Molecules Ionic and covalent bonds The Simple
Hückel Method and Applications Benzene and
One-Dimensional Solid. Fundamental Concepts of
Spectroscopy and Photochemistry Quantum Mechanics
of Light Absorption The Einstein Coefficients
Correlation between Spectra and Molecule
Structures Principle of Lasers Photochemical
Processes Application on Solar Cells.
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Energetics, Entropy and Free Energy Brief
Revision of the three Laws of Thermodynamics
Definition of System Equation of State and
States Variables Concepts of Equilibrium
Correlation between Microscopic and Macroscopic
Properties Brief Concepts of Termodynamic
Statistics. Kinetics and Catalysis The Rate of
Chemical Change Concepts of Activation Energy
Homogeneous and Heterogeneous Catalysis
Electrocatalysis Application on Fuell Cells
Electrical Fields and Potentials at Interfaces
Search of new Materials with catalytic Properties.
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Position, mass, velocity, charge, spin
Particle theory
Two opposing concepts
Quantum Mechanics
Field theory
Functions continuous in space and time
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Einstein
Bohr
Heisenberg
Planck
Photons
de Broglie
electrons
Schrödinger
Energy
Waves
Uncertainty
diffraction
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Quantum Mechanics
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Quantum Mechanics
If therefore angel area not composed of matter
and form, as was said above, it follows that it
would be impossible to have two angels of the
same species... The motion of an angel can be
continuous or discontinuous as it wishes... And
thus an angel can be at one instant in one place,
and at another instant in another place, not
existing at any intermediate time Thomas
Aquinas, Summa Theologica, 1268
Nature does not make a Jump
Energy Continuous Matter
Discrete
Classical Mechanics
Quantum Mechanics
Energy Continuous
only in discrete units called Quanta

• Duality Behaviour Wavelike ? Particlelike

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Black-Body Radiation
A blackbody is a hypothetical object that absorbs
all incident electromagnetic radiation while
maintaining thermal equilibrium. 
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Black-Body Radiation classical theory
Radiation as Electromagnetic Waves
1D
3D
Since there are many more permissible high
frequencies than low frequencies, and since by
Statistical Thermodynamics all frequencies have
the same average Energy, it follows that the
Intensity I of balck-body radiation should rise
continuously with increasing frequency.
Breakdown of classical mechanical principles when
applied to radiation
!!!Ultraviolet Catastrophe!!!
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The Quantum of Energy The Planck Distribution
Law
Physics is a closed subject in which new
discoveries of any importance could scarcely
expected.
However He changed the World of Physics
Nature does not make a Jump
Matter Discrete Energy
Continuous
Classical Mechanics
Max Planck
Energy Continuous
Planck Quanta
E hn
h 6.6262 x 10-34 Joule.sec
An oscillator could adquire Energy only in
discrete units called Quanta
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Some concepts about waves.
Wave
The propagation of a perturbation. It is also a
way to transport Energy. Periodic changes in
Space and Time of some Property. There is no net
displacement of the medium
tfinal(x2-x1)/v
t0
tfinal
t0
X2
X1
Shape of the disturbance
Profile of the wave such as an instantaneous
snapshot of the wave form. It repeats
periodically in Time and Space.
Wave Function
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Particular Pattern Sinusoidal Waves. These
waves are called Harmonic Waves.
Harmonic Waves? Sinusoidal Waves
Temporal Period
Spatial Period or Wavelength
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Amplitude
Phase
Angular Wave Number or propagation Number
Frequency
Angular Frequency
Wave Number
Phase Velocity
Temporal Period
v
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A central concept of Quantics waveparticle
duality is the concept that all matter and
energy exhibits both wave -like and particle
-like properties.
The Wave Nature of Matter
All material particles are associated with
Waves (Matter waves)
E hn E mc2
mc2 hn hc/l or mc h/l
Planck
Einstein
De Broglie
A normal particle with nonzero rest mass m
travelling at velocity v
mv p h/l
Then, every particle with nonzero rest mass m
travelling at velocity v has an related wave l

• Duality Behaviour Wavelike ? Particlelike

l h/ mv

• The particle property is caused by their mass.
• The wave property is related with particles'
  electrical charges.
• Particle-wave duality is the combination of
  classical mechanics and electromagnetic field
  theory.

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Energy
only in discrete units called Quanta
E hn
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• Duality Behaviour Wavelike ? Particlelike

l h/ mv
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Wave Function
Differential Wave Equation
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Travelling / Standing Waves
When the primary and reflected Waves have the
same A and speed v It vibrates in place. Nodes
Places where the medium does not ever vibrate.
Standing Waves
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Differential Wave Equation
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Space f(x)
TIme f(t)
Equivalent to two ordinary (not partial)
differential equations
Space X(x)
Time T(t)
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Standing Waves
Boundary Conditions
XL
X0
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Solution of the Differential Wave Equation
Eigenvalue Condition
n0, 1, 2, 3
Eigenfunctions
Since any linear Combination of the
Eigenfunctions would also be a solution
General solution Principle of superposition
Fourier Series
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Fourier Series
Any arbitrary function f(x) of period L can be
expressed as a Fourier Series
REAL Fourier Series
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The superposition of a group of waves differing
from each other in wavelength yields a Wave Packet
Wave Packet
two waves can interfere to form another, more
complex wave. If we add enough waves together, we
can make a wave packet with a range of locations
that's as small as we want.
A wave packet is a localized disturbance that
results from the sum of many different wave
forms. If the packet is strongly localized, more
frequencies are needed to allow the constructive
superposition in the region of localization and
destructive superposition outside the region.