Short run equilibrium
First of all, we need to look at the possible situations in which firms may find themselves in the
short run.
With each of the three diagrams above, the situation for the firm is only drawn. The 'market'
diagram, from which the given
The Sweet Hereafter is a novel by Russell Banks exploring the community reaction to a school bus
accident that kills fourteen children. Written from four perspectives, the book shows how a common
event effects lives differently and on a varying scale. Nar
The following features a discussion between the interviewer
Kate Davis and the author Jim Beamon about the preparation
and conducting of the interview from the interviewers point of
view.
Interviewer: Okay, Kate. So, you've just interviewed Sharon
about c
Question 1 :Remember that current is the flow of electrons. If one Coulomb of electrons goes
past a certain point every second, then we say the current at that point is 1
Ampere.
A light bulb is a simple apparatus that converts electric energy into light
68 95 99.7 Rule in Statistics
When you use a standard normal model in statistics:
About 68% of values fall within one standard deviation of the mean.
About 95% of the values fall within two standard deviations from the mean.
Almost all of the values about
Suppose that, at the current price of $1.50 per gallon and average household income of $100,000 a
year, the quantity demanded of bottled water is 200 million gallons a week. If the price were increased
to $1.68, the quantity demanded would fall to 158.7 m
Homework #5
1. What is the Income Effect?
The income effect represents the change in an individual's or
economy's incomeand shows how that change impacts the quantity
demanded of a good or service.
2. What is the Substitution Effect?
The substitution effe
He says that he cant exactly remember the genesis of Model Behavior,
although I would say at this distance that it was an attempt to reclaim
the material of my youth and write one more book about an
irresponsible post-adolescent who has yet to sign the s
Lecture 7: Angular Momentum, Hydrogen
Atom
1
Vector Quantization of Angular Momentum and Normalization of 3D Rigid Rotor
wavefunctions
Consider l = 1, so L2 = 2~2 . Thus, we have |L| = ~ 2. There are three
possibilities for Lz depending on the value of ml
Lecture 5: Harmonic oscillator
It turns out that the boundary condition of the wavefunction going to
zero at infinity is sufficient to quantize the value of energy that are allowed.
1
Ev = v +
~
v = 0, 1, 2, .
2
p
where = k/m is the angular frequency of t
Lecture 1: Quantum Mechanics: Origins and theory.
1
Status of Physics around 1900
It is not an exageration to say that Physics was in a very sound state towards the end
of the 19th century. Particle mechanics was soundly explained using Newtons laws of
mo
Lecture 2: Operators, Eigenfunctions and the
Schrodinger Equation
1
Operators, eigenfunctions, eigenvalues
Corresponding to every physical obervable in Classical Mechanics, there is an operator
in quantum mechanics which operates on the wavefunction(state
Lecture 8: Radial Distribution Function,
Electron Spin, Helium Atom
1
Radial Distribution Function
The interpretation of the square of the wavefunction is the probability density
at r, , . However, if we ask about the probability of finding at a given r
i
Lecture 4: Particles in a 2D box, degeneracy,
harmonic oscillator
1
Particle in a 2D Box
In this case, the potential energy is given by
V (x, y) = 0 0 x a, 0 y b
= otherwise
The Hamiltonian operator is given by
2
~2
d
d2
+
+ V (x, y)
2m dx2 dy2
and the c
Lecture 6: 3D Rigid Rotor, Spherical
Harmonics, Angular Momentum
We can now extend the Rigid Rotor problem to a rotation in 3D, corresponding to motion on the surface of a sphere of radius R. The Hamiltonian
operator in this case is derived from the Lapla
Lecture 3: Particle in a 1D Box
First we will consider a free particle moving in 1D so V (x) = 0. The
TDSE now reads
~2 d2 (x)
= E(x)
2m dx2
which is solved by the function
= Aeikx
where
k=
2mE
~
A general solution of this equation is
(x) = Aeikx + Beikx
Lecture 9: Molecular Orbital theory for
hydrogen molecule ion
1
Molecular Orbital Theory for Hydrogen Molecule
Ion
We have seen that the Schrodinger equation cannot be solved for many electron systems. The H+
2 molecule ion is a molecule that has only one
Lecture 10: Molecular Orbital Theory for
Homonuclear Diatomic molecules
The MO theory can be generalized to many electron atoms. Here the
atomic orbitals will have the same quantum numbers as those of hydrogen
but can be quite different. If we use the bas
Chapter 7
Particle on a Sphere
7.1
Particle on a Sphere: Schrdinger Equation
Let us consider a particle confined to move in three dimensions, but on a sphere of
radius r. Let there be no external potential acting on the system. The Hamiltonian
operator of
Lecture 5
Particle in 3D Box and Harmonic
Oscillator
5.1
Particle in a Three-Dimensional Box
Here,
V ( x, y, z) =
0
if 0 < x < L x , 0 < y < Ly , and 0 < z < Lz
(5.1)
otherwise
h 2 2
h 2 2
h 2 2
H =
2m x2 2m y2 2m z2
2
h 2
2
2
+
+
=
2m x2 y2 z2
h 2
Lecture 2
Schrdinger Equation
2.1
The Schrdinger Wave Equation (1926)
Heisenberg and Schrdinger have independently developed theories that looked very
different, but correctly account for the wave like properties of microscopic systems.
Here we will consi
Lecture 3
Particle in a Box
In the coming few chapters, we will solve Schrdinger equation (SE) for various simple
model systems (with increasing complexity).
The recipe for solving SE is as follows:
Define the potential energy function (system dependent)
Lecture 1
Introduction to Quantum Mechanics
Important Notes:
Reference books:
Physical Chemistry, by P. Atkins and J. de Paula
Physical Chemistry, by I. N. Levine
Physical Chemistry; A Molecular Approach, by D. A. McQuarrie and J. D.
Simon
Memorize t
Lecture 4
Particle in 2D Box
4.1
Particle in a Two-Dimensional Box
Let us consider a particle within a two dimensional box, defined by the wall po-
y
Ly
tentials
V ( x, y) =
0
V =0
if 0 < x < L x & 0 < y < Ly
V =1
(4.1)
otherwise
0
Lx
x
You can visuali
Lecture 6
Particle in a Ring
6.1
Particle in a Ring: Schrdinger Equation
Let us consider a particle confined to move in a ring of radius r, lying in the x y
plane. Let us also consider that no potential is acting on the system. The Hamiltonian
operator of
CHM102A GeneralChemistry
CHM102A
General Chemistry
Part 1: Inorganic and Organic Chemistry
Ramesh Ramapanicker
Part 2: Physical Chemistry
Madhav Ranganathan
Inorganic/Organic Section A
Lectures: MW 9:00-9:50 (L7); Tutorial: F 9:00-9:50 (L3, L4, L5 and L6)
Relation Between Substituents on Cyclohexane
Interaction Energies of Substituents on Cyclohexane
If substituents are very large, the instability of the axial conformer becomes high
enough to not have a chair conformation at all.
pp if substituents (even i
Conformations of Cycloalkanes
Cycloalkanes are not always planar structures. Being planar requires large variations in
bond angles from the ideal value of 109.5 for a tetrahedral carbon.
Cyclopropane
Cyclopropane
C
l
has
h a high
hi h degree
d
off torsion