Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 1
1. [10] A particle of mass m lies in one-dimension in a potential of the form V(x) =
Fx, where F is constant. The wave function at time t is given by
x, t N t exp 1 A t x 2 B t x
2
where N,
1/26/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 7:
Start reading Chapter 3
Solution of Poisson equation in for
special geometries
A. Cylindrical
B. Spherical
01/27/2017
PHY 712 Spring 2017 - Lecture 7
1
01/27/2017
PHY 712 Spring
1/19/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 4:
Reading: Chapter 1 & 2 in JDJ
Electrostatic potentials
1. One, two, and three dimensions
(Cartesian coordinates)
2. Mean value theorem for the
electrostatic potential
1/20/2017
P
1/28/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 8:
Start reading Chapter 4
Multipole moment expansion of
electrostatic potential
A. Spherical coordinates
B. Cartesian coordinates
01/30/2017
PHY 712 Spring 2017 - Lecture 8
1
01/3
Numerical methods to solve Poisson and Laplace equations; Finite difference
methods
The basis for grid-based finite difference methods is a Taylors series expansion:
1
1
1
(u)2 (r)+ (u)3 (r)+ (u)4 (r)+ .
2!
3!
4!
(1)
For the 2-dimensional Poisson equation
2/3/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 10:
Complete reading of Chapter 4
A. Microscopic macroscopic
polarizability
B. Clausius-Mossotti equation
C. Electrostatic energy in
dielectric media
02/03/2017
PHY 712 Spring 2017 -
2/6/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 11:
Start reading Chapter 5
A. Magnetostatics
B. Vector potential
C. Example: current loop
02/06/2017
PHY 712 Spring 2017 - Lecture 11
1
02/06/2017
PHY 712 Spring 2017 - Lecture 11
2
1/9/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 1:
Reading: Appendix 1 and Chapters I&1
1. Course structure and expectations
2. Units SI vs Gaussian
3. Electrostatics Poisson equation
1/11/2017
PHY 712 Spring 2017 - Lecture 1
1
1/
1/18/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 3:
Reading: Chapter 1 in JDJ
1. Review of electrostatics with onedimensional examples
2. Poisson and Laplace Equations
3. Greens Theorem and their use in
electrostatics
1/18/2017
PH
1/25/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 6:
Continue reading Chapter 2
1. Methods of images - planes,
spheres
2. Solution of Poisson equation in
for other geometries - cylindrical
1/25/2017
PHY 712 Spring 2017 - Lecture 6
1/11/2017
PHY 712 Electrodynamics
9-9:50 AM MWF Olin 103
Plan for Lecture 2:
Reading: Chapter 1 (especially 1.11) in JDJ;
Ewald summation methods
1. Motivation
2. Expression to evaluate the electrostatic
energy of an extended periodic system
3. Examples
1
Lecture 7 Notes
Particle nature of light was proposed by Einstein in 1905 to explain the photo-electric
effect. Photo-electric effect automatic door openers in grocery stores. Particles of light
are called light quanta or photons.
Energy of a Photon = h (
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 2
1. [10] A free particle of mass m in one dimension takes the form at t = 0
x, t 0 x A exp iKx 1 Ax 2
2
1/ 4
Note that this is identical with chapter 1 problem 4. Find the wave at all
subseq
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 3
1. [10] Prove Schwartzs inequality, , , , , . You may prove it
however you want; however, here is one way to prove it. Expand out the inner
product of a b with itself, which must be positive,
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 5
1. [15] The Lennard-Jones 6-12 potential is commonly used as a model to describe
the potential of an atom in the neighborhood of another atom. Classically, the
12
6
energy is given by E 1 mx
Physics 741 Graduate Quantum Mechanics 1
Solutions to Chapter 6
1. [10] For the finite square well in section C, we showed that (6.24) is satisfied for
the even wave functions. Repeat this derivation for the odd wave functions; i.e.,
derive (6.25).
We kno
Physics 742 Graduate Quantum Mechanics 2
Solutions to Final Exam, Spring 2010
Due Friday, May 7
You may use (1) class notes, (2) the text, (3) former homeworks and solutions (available
online), or (4) any math references, such as integral tables, Maple, e
Physics 742 Graduate Quantum Mechanics 2
Final Exam, Spring 2010
Due Friday, May 7
You may use (1) class notes, (2) the text, (3) former homeworks and solutions (available
online), or (4) any math references, such as integral tables, Maple, etc, including
Lecture 3 Notes
Quantum theory is a theory needed to describe physics on a
microscopic scale, such as on the scale of atoms, molecules,
electrons, protons, etc.
Classical theories:
Newton Mechanical motion of objects (F = ma)
Maxwell Light treated as a wa
Lecture 4 Notes
Photons can be treated as packets of
light which behave as a particle.
To describe interactions of light with matter, one generally has to
appeal to the particle (quantum) description of light.
A single photon has an energy given by
E =
Chronic Diseases
Cardiovascular Disease
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What are the two types of CVD? Coronary artery
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