PHY-852 QUANTUM MECHANICS II
Homework 6, 40 points
February 23 - March 2, 2011
Identical particles
Reading: Quantum Physics, Volume 2, Sections 15.1-4, 17.1-4, 18.1-3
1. /10/ a. Consider a system of two identical particles of arbitrary spin s.
Find the nu
PHY-852 QUANTUM MECHANICS II
Homework 7, 40 points
March 14 - 23, 2011
Discrete spectrum and variational method
Reading: Quantum Physics, Volume 1, Sections
3.1-3; 3.5; 5.6; 10.1-3; 11.1; 17.1-4
1. /6/ For a particle bound in the potential box (0 < x < a)
PHY-852 QUANTUM MECHANICS II
Homework 5, 40 points
February 16 - 23, 2011
Symmetries and spins
Reading: Quantum Physics, Volume 1, Sections 8.3-5, 16.1-10, 20.2-3
1. /8/ A non-relativistic neutron (spin magnetic moment ) is moving in an
axially symmetric
PHY-852: QUANTUM MECHANICS II
Quiz 7
April 1, 2011
NAME.
PROBLEM. A particle of mass m and electric charge e is placed in the onedimensional harmonic oscillator potential of frequency . The uniform electric
field E is applied along the same axis.
a. Find
PHY-852: QUANTUM MECHANICS II
Quiz 6
March 25, 2011
NAME.
PROBLEM. A quantum harmonic oscillator with mass m and elastic force
kx is perturbed by a small change k k + . Using perturbation theory
find the change of the energy spectrum and compare the resul
PHY-852 QUANTUM MECHANICS II
Homework 9, 40 points
March 30 - April 6, 2011
Stationary perturbations
Reading: Quantum Physics
Volume 1, Sections 4.7, 16.6-16.7, 17.6, 19.1-19.4, 24.1-24.4
1. /12/ An electron is confined to a circle of radius R in the xy-p
PHY-852: QUANTUM MECHANICS II
Quiz 3
February 11, 2011
NAME.
PROBLEM. Consider two Hamiltonians of a non-relativistic particle of
spin 1/2 which consist of kinetic energy, spin-independent central potential and
different spin-dependent potentials,
a.
2
1
PHY-852: QUANTUM MECHANICS II
Quiz 1
January 28, 2011
NAME.
PROBLEM. a. Calculate the mixed product of three Pauli matrices
A = ~ [~ ~ ] .
(1)
b. Reduce to the form linear with respect to the Pauli matrices the operator
k = (a ~ )k ,
B
(2)
where a is a nu
PHY-852: QUANTUM MECHANICS II
Quiz 4
February 18, 2011
NAME.
PROBLEM. A proton state is characterized by the momentum p along the
z-axis and by the certain value h = +1 of the helicity [projection h = (~ p)/|p|
of the proton spin (s = (1/2)~ ) on the dire
PHY-852: QUANTUM MECHANICS II
Quiz 2
February 4, 2011
NAME.
PROBLEM. For the following operators find out if they correspond to conserved quantities for free motion of a relativistic particle of spin 1/2:
2
a. orbital momentum squared ~` ,
b. spin squared
PHY-852 QUANTUM MECHANICS II
Midterm test
March 4, 2011
Total 30 points
NAME.
1. Write down the Dirac equation for a particle moving in a spherically symmetric electrostatic potential (r). List all constants of motion.
2. Consider a system of two particle
PHY-852 QUANTUM MECHANICS II
Homework 4, 40 points
February 9 - 16, 2011
Symmetries
Reading: Quantum Physics, Volume 1, Sections 7.10, 8.1-5, 16.1-16.4, 20.5-6
1. /32/ Consider the set of physical quantities describing the motion of a
spinless charged par
PHY-852 QUANTUM MECHANICS II
Homework 2, 40 points
January 26 - February 2, 2011
Klein-Gordon-Fock equation. Spin 1/2
Reading: Quantum Physics: Volume 2, Section 11.10;
Volume 1, Sections 16.1-16.4, 20.1-20.3
1. /12/ a. In the Problem 11.1 (Volume 2) it i
PHY-852 QUANTUM MECHANICS II
Homework 1, 40 points
January 19 - 26, 2011
Klein-Gordon-Fock equation (KGFE)
Reading: Quantum Physics, Volume 2, Sections 11.1-11.10.
1. /10/ a. Consider a particle of mass m and electric charge e moving in
an electrostatic p
Variational method and diagonalization
Take a complete orthonormalized set of states |ni. Select N states of this
set, |1i, |2i, ., |N i, and look for the approximate solution of the stationary
Schr
odinger equation,
= E,
H
(1)
in the form of the superpo
PHY-852: QUANTUM MECHANICS II
Quiz 5
March 18, 2011
NAME.
PROBLEM. Consider a neutron in the gravitational field near the surface
of the Earth. Estimate the energy of its quantum ground state using the variational method with a reasonable (and simple enou
Lecture 4 part 2
Secondary active transport
at apical domain
Na+, K+ pump in
basolateral (creates Na+ gradient used for secondary active transport)
Cystic Fibrosis is due to
recessive mutation in CFTR gene (disease of epithelial ion trasnport)
What popula
Lecture 4 part 1
Three cell types
epithelia, neuron, muscle
Epithelia
specialized for transport and secretion, polarity of epithelial cells and tissue
is a fundamental trait
Epithelial transport
polar organization of transporters achieves transcellular tr
Lecture 8 Notes
cholinergic
releasing or activated by acetylcholine or a related compound
Secretion in general is stimulate by
increase in [Ca+]i
Vesicular secretion
SNARES mediate membrane fusion as a result, in part, of stimulation of Ca
Fluid Secretion
Lecture 15 Notes
Nociceptor reflex: Noxious stimulus
flexion or withdraw from the stimulus
Myotatic reflex: Stretch of muscle
contraction of the same muscle
Pupillary light reflex: Bright light
pupils constrict
Thermoregulatory reflexes
Heat stress sweati
Lecture 14 Notes
CNS
Brain + Spinal Cord
CNS Contains
Blood vessels, connective tissue, glial cells, neurons,
glial cell
Cells in the nervous system that support, nourish, and protect neurons
Gray Matter
General term for area that is mostly neuron cell bo
Lecture 13 Notes
skeletal muscle
ca+ release from SR by unusual mechanical mechanism, similar to toilet
plugner, b/c Ca+ release is satrating, strength of contraction not controlled
by Ca+ levels
Cardiac muscle
Ca+ induced Ca+ release (CICR) from SR, usin
Lecture 11 Notes
Action potential coding
all or nothing property of APs means that code, at some level, must be
simpler than Morse code-there are only 'dots', simple examples is touchtypical of sensory encoding
Four attributes of sensory input encoded by
Lecture 6 Notes
Receptors
usually denote proteins molecules specialized specifically for information
reception and trasduction from ECF
Intercellular (between cells) signaling molecules bind to these antenna
molecules
to initiate response inside the cells
Lecture 7 Notes
G-protein coupled receptor (GPCRS)
are largest and most diverse type of receptor family, arguably the most
important 40-50% of all therapeutic drugs on the market act via their effect
on a G-protein signal pathway
GPCRs
G-proteins coupled