By the beginning of the 20th century life in physics was simple.
Electromagnetic radiation was waves, electrons were particles
Probability was tolerated (e.g. in statistical physics) as a way to deal with inability
to solve ~1023 equations of motion. Or j
*Problern 4,27 n elevation is in the spin state-
(3 Determine the normalization Constant.- A;
(1) Find the expectation values of SI, 3, and SP
cfw_c Find the uncertainties as, orgy, and 0:53. (Note; These sigmas are standard
deviations, notPfauli in
See pages 78 and up for even solutions.
Continuation / related problem: Suppose we are dealing with half-infinite well (L=a from above)
Prove without any calculations that there are no bound states unless L=a>/2
Consider the wavefunctions of the finite-we
PHYS 377 Assignment 2
Due: Thursday 1 October 2015
A free particle has the wave function
(x, 0) = Aeax ,
where A and a are constants (a is real and positive).
(a) Normalize (x, 0).
(b) Find (x, t). Hint: Integrals of the form
PHYS 377 Assignment 1
Due: Thursday 24 September 2015
Consider the wave function
(x, t) = Ae|x| eit ,
where A, and are positive real constants.
(a) Normalize .
(b) Determine the expectation values of x and x2 .
(c) Find the standard deviation of
PHYS 377 Assignment 3
Due: 8 October 2015
Derive Equations 2.167 and 2.168. Hint: Use Equations 2.165 and 2.166 to solve for C
and D in terms of F :
C = sin(la) + i cos(la) eika F ;
D = cos(la) i sin(la) eika F.
Plug these back i
Problemsolving in Class 3
Maybe going through the sum and product of two Hermitian operators?
(a) The sum of two hermitian operators is also hermitian. From the definition:
is hermitian, then
is hermitian if is real. First we note:
Problems in class:
Wavelength 2000A=200 nm, so the frequency is c/lambda=1.5x10^15 Hz.
Energy of a photon 9.945x10-19 Joule
Electrons can be stopped by the potential of 4.21 V if their energy was 4.21 eV or 6.736x10-19 Joule
Thus, work function of cesium
Griffiths 1.5 Consider the Wave function (see Eq 1 below). Normalize. Determine the
expectations of x and x2 Find the standard deviation of x.
Griffiths 2.4. Find expectations and variances of x and p for n-th stationary state of the
infinite square well
Problemsolving in Class 12/10/2016
Suppose we have
as a free particle?
. How far can we get in working out this systems behaviour
First, we need to normalize the initial condition, so we do the usual integral
Next, we can use Plancherels theorem to work o
This is the part of the Clebsch-Gordan table that one has to use, the one corresponding to
adding angular momenta 1 (orbital, lower index of spherical harmonics) and (spin of an
electron). NB: these tables can be used to add any kinds of angular momenta,
Lecture 2: Introduction to probabilities.
Gambling: the driving force behind early research in
Blaise Pascal, Pierre Fermat, etc had to answer questions like Suppose the game
has to be stopped before anyone wins. How to divide the money?
Wave (Optics) Reminder
Wave equation can be derived from Maxwells equations.
Wave equation is linear: any linear superposition of the solutions is also a
(r , t ) Ci i (r , t )
The Addition of Waves of Different Frequency
Time Independent Schrdinger Equation
How does one solve the SE for a particular shape of potential energy V(x)?
If V is independent on t, one can attempt separation of variables
Only a tiny subset of solutions can be factored this way.
But these are usefu
Basics of Quantum Mechanics
- Classical Point of View In Newtonian mechanics, the laws are written in terms of PARTICLE
A PARTICLE is an indivisible mass point object that has a variety of properties
that can be measured, which we call obser
PHYS377 Quantum Mechanics I.
What it contains: Schrdinger equation, probabilistic interpretation, normalization,
expectation values, the uncertainty principle, stationary states, the free particle, infinite
square well, the finite square well, t
*Problem 6.1 Suppose we put a delta-function bump in the center of the innite
H' = 0:50: (1/2).
where is is a constant.
(3) Find the rst-order correction to the allowed energies. Explain why the ener-
gies are not perturbed for even :1.