Lecture 3 Notes: Classic Energy Functions
p2
p2
p2
K
2 2
1
2
1
E 2 V x
Kx 2 m x H x, p,
m
2m 2
m 2
m
Using the Hamiltons equations one can solve for the classical
trajectory:
p
x t x(t
dx H
2
2
0)cost
dt p m
K
2 x
dx
dx
x
0
2
2
dp H K
m
pt x(t 0)
Lecture 9 Notes: Donor Atoms
Semiconductor carrier engineering: Extrinsic Semiconductors
Adding very small amounts of impurities can drastically change the conductivity
of the semiconductor and define the conduction type, i.e. make it largely
electron-con
Lecture 10 Notes: Ferromagnetic Atoms
When sufficiently large external magnetic field is applied, the magnetic
dipoles will start to orient parallel to the field. Eventually when all
magnetic dipoles are oriented parallel to the field the magnetization of
Lecture 7 Notes: Symmetrization
Two particles are identical if their intrinsic properties are the same
and we cannot set up an experiment to distinguish them.
In Quantum Mechanics we cannot distinguish between electron within the
same potential.
Example:
Lecture 8 Notes: Parameter Definitions
probability of two particles in
the same state probability of
two particles in different
states
1
MB 2 , BE 1, FD 0
Compared to the classical case the bosons tend to bunch while fermions
(electrons) remain apart.
Now
Lecture 6 Notes: Effective Mass Ratios
Away from the band edges the electron has a finite and nonzero group velocity as the band edge
is approached the group velocity decreases until it is equal to zero. This means that electrons that
have Bloch wave eige
Lecture 5 Notes:
Harmonic
Functions
12
2
e 2r r
2
Akin to the harmonic oscillator eigenfunctions and the spherical harmonics the solution of the
radial equation is obtained by a power series expansion method.
Then the complete eigenfunctions and eigenvalu
Lecture 4 Notes: General Schematics
i1
Finding the eigenvectors and eigenvalues of operators, discuss the geometrical interpretation of
eigenvectors and eigenvalues scaling.
Fourth Postulate (discrete non-degenerate): When the physical quantityais measure
Lecture 2 Notes: Plancks Philosophy
In 1900, Planck proposed a revolutionary idea: Electromagnetic energy is quantized!
There
are portions or quanta of energy photons with energy:
34 2
Ephh2cch,h6.6310 m kg/s1.061034m2kg/s
2
2
Here h is a Plancks constant
Lecture 1 Notes: Intro to Course
the application of Hamiltons equations we derive the equations of motion:
dps
H
us dt
H dus
ps
dt
Focus on the terms in the Hamiltonian that contain us and ps
1
1
2
2
ps2
K us1 us K us u s1 .
2m
2
2
We then obtain:
dus ps