1.Historical introduction to quantum mechanics

nothingstockingsMechanics

Oct 30, 2013 (4 years and 8 days ago)

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1.

Historical introduction to quantum mechanics


blackbody radiation, Wien displacement law, Boltzmann law, Planck’s formula, Einstein
contribution to description of blackbody radiation, photoelectric effect, Compton effect


2.

Waves as particles and particles
as waves


photon energy, photon momentum, energy
-
frequency dependence, matter waves, de Broglie
relation, Davisson
-
Germer experiment


3.

The Schrödinger equation


particles as waves


description of interference experiment, probabilistic interpretation of
wav
e functions, time
-
dependent

Schrödinger equation, representation of plane waves,
separation of Schrödinger equation, time
-
independent Schrödinger equation, eigenfunctions
and eigenvalues of the Hamiltonian, infinite quantum well, quantization of energy


4.

Wa
ve packets and the uncertainty principles


construction of wave packets, Heisenberg position
-
momentum uncertainty relation,
Heisenberg microscope, interpretation of two
-
slit experiment, time
-
energy uncertainty
relation and its consequences


5.

Barriers and we
lls


solution

of Schrödinger equation for
rectangular
potential barrier, tunneling: theory and
examples: alpha decay, nuclear fusion, scanning tunneling microscope STM, finite quantum
well
-
bound states, electron traps: nanocrystallites, quantum dots, quant
um corral


6.

Models of simple atoms


degenerate state, early models of atoms, Bohr theory of hydrogen atom, quantization of
angular momentum (one of the postulates), energy levels, interpretation of emission and
absorption spectra of atoms, correspondence pr
inciple


7.

Hydrogen atom in quantum mechanics


solution

of Schrödinger equation for central Coulomb potential, radial functions and spherical
harmonics, quantum numbers, energy eigenvalues for hydrogen, angular momentum, orbital
magnetic dipole moment, elect
ron spin,
application of theory:
Nuclear Magnetic Resonance
NMR


8.

Many particles


complex atoms

and molecules


multiparticle Schrödinger equation, independent particles, identic
al particles, symmetric and
anti
symmetric wave functions, fermions and bosons,
Pauli exclusion principle and
consequences, Fermi energy, periodic table, complex atoms, ordering of elements, simple
model of H
2

molecule, binding energy, chemical bonding, ionic crystals,
covalent bonding,
metals, van der Waals forces, hydrogen bonded cr
ystals, vibrational and rotational levels


9.

Statistical physics


classical gas: Maxwell distribution of molecular velocities, Boltzmann distribution, quantum
statistics: Fermi
-
Dirac and Bose
-
Einstein distribution functions, applications: specific heat of
el
ectrons in metals, Bose
-
Einstein condensation, liquid helium and superfluidity


10.

Electrical conductivity of solids


characterization of insulators, metals, semiconductors, band structure of solids, intrinsic and
extrinsic semiconductors, temperature
depende
nce
of the electrical conductivity, definition of
carrier mobility, mechanism of scattering, Matthiessen rule,
p
-
n junction, majority and
minority charge carriers, diffusion and drift currents, some basic applications of
semiconductors: junction rectifier,

light


emitting diode LED, field effect transistor FET