Physics 520
Introduction to Quantum Mechanics
Fall 2018
Home Page: http://www.pa.uky.edu/~gardner/p520/
MWF: 11:00 - 11:50PM, CP 287
Syllabus
Introduction to Quantum Mechanics
Fall 2018
Home Page: http://www.pa.uky.edu/~gardner/p520/
MWF: 11:00 - 11:50PM, CP 287
Syllabus
General Information:
Lecturer: Prof. Susan Gardner
Required textbook:
Recommended textbook:
Physics 520 is a semester's introductory course in quantum mechanics.
Knowledge of modern physics at the level of Phy 361 is required, and
familiarity with differential equations at the level of Ma 214 is also
essential.
The behavior of physical systems at the nanometer scale is strikingly
counterintuitive to those well-versed in the study of classical
phenomena. Yet ``strange'' as these systems may be, their behavior
can be understood in the context of a theoretical framework with
genuine predictive power.
It is our purpose to construct such a quantum mechanics and
to investigate its consequences for physical systems operating at the
nanometer scale.
A bevy of texts, of varying sophistication and coverage of applications,
exist in the literature. An annotated bibliography of them has been included
in the course web site.
We will begin by reviewing the empirical need for a quantum mechanics and
indeed shall emphasize
the empirical ramifications of the quantum
phenomena described throughout the course. The lectures will blend material from
Griffiths and Gasiorowicz, particularly at the beginning of the course.
It has been the fashion - for many decades - to
emphasize the mathematical structure of quantum mechanics
in introductory courses to the topic, so that much attention is paid
to the solution of Schroedinger's equation in various contexts.
This tends to underscore the commonality of quantum mechanics
with classical physics, and we will certainly be traditionalists in this regard.
Nevertheless, the probabilistic aspects of
quantum physics make it profoundly different from classical physics.
Moreover, in recent decades tremendous progress has been made in the
understanding of quantum mechanics and in the ability to manipulate
atoms at subatomic scales, with extraordinary
technological ramifications which are still unfolding.
Office: Blazer 351
Phone: 257-4391
E-mail: gardner at pa dot uky dot edu
Office Hours: T, Th from noon to 1PM and from 5-6PM and by appointment.
D. J. Griffiths and D. F. Schroeter,
Introduction to Quantum Mechanics, Third Ed. (2018)
S. Gasiorowicz
Quantum Physics, Third Ed. (2003)
Course Description and Prerequisites
Course Topics:
| Wave packets and uncertainty relations. |
|---|
| The Schroedinger equation. |
| Simple problems. Wells, barriers, harmonic oscillator. |
| Postulates. Basic postulates; interpretation. Time evolution. |
| Mathematical tools. Ket and bra vectors, operators, state spaces. |
| Two-level systems. Spin 1/2 particles. Neutral K and B mesons. |
| The harmonic oscillator via various techniques. |
| Angular momentum. Rotations, states, operators, representations. |
| Central potentials. H-atom, muonium. |
| Matrix Methods. Spin. |
Note that the course continues into a second semester, via Phy 521, Introduction to Quantum Mechanics II. The following topics will be addressed: scattering by a potential, addition of angular momenta, systems of identical particles, perturbation theory, variational methods, H-atom fine and hyperfine structure, Zeeman and Stark effects, and the interaction of atoms with radiation.
Lecture Schedule
The reading assignments and lecture plan will generally be posted ~1 week before the lecture in question. "G" denotes Gasiorowicz. "GS" denotes Griffiths and Schroeter.
[Updated: 11/26/18]
| Date | Reading | Description | ||
|---|---|---|---|---|
| W Aug. 22 | Ch. 1 (G) | Introduction | ||
| F Aug. 24 | Ch. 1 (G) | Blackbody Radiation | ||
| M Aug. 27 | Ch. 1 (G) | Blackbody Radiation; Photoelectric Effect | ||
| W Aug. 29 | Ch. 1 (G) | The Photon; Compton Effect | ||
| F Aug. 31 | Ch. 1 (G) | The Correspondence Principle | ||
| M Sep. 3 | Labor Day, Academic Holiday | |||
| W Sep. 5 | Ch. 1 (GS) | Two-Slit Experiments: Probability Distributions | ||
| F Sep. 7 | Ch. 1; 2.4 (GS); Ch. 2 (G) | Wave Packets | ||
| M Sep. 10 | Ch. 2 (GS) | Fourier Transforms: Wave Packets in x- and p-space | ||
| W Sep. 12 | Ch. 2 (GS) | Wave Packets & The Uncertainty Principle | ||
| F Sep. 14 | Ch. 1, 2 (GS) | The Schroedinger Equation; Probability Interpretation | ||
| M Sep. 17 | Ch. 1, 2 (GS); Ch. 2,3 (G) | Uncertainty Principle Estimates | ||
| W Sep. 19 | Ch. 1, 2 (GS); Ch. 2,3 (G) | Expectation Values | ||
| F Sep. 21 | Ch. 1, 2 (GS); Ch. 2,3 (G) | Operators; Commutation Relations <\th> | ||
| M Sep. 24 | Ch. 1, 2 (GS); Ch. 2,3 (G) | Ehrenfest's Theorem; Time-Independent Sch. Eqn. | ||
| W Sep. 26 | Ch. 1, 2 (GS); Ch. 2,3 (G) | Eigenvalue Problems; The Particle in a Box | ||
| F Sep. 28 | Ch. 1, 2 (GS); Ch. 3 (G) | The Particle in a Box (cont.) | ||
| M Oct. 1 | Ch. 3 (G) | Eigenfunctions as a ``Basis'' | ||
| W Oct. 3 | Ch. 3 (G) | Postulates of QM; Observables | ||
| F Oct. 5 | Ch. 3 (G) | Parity; Simultaneous Eigenfunctions; Plane Waves to Wavepackets | ||
| M Oct. 8 | Ch. 2 (GS); Ch. 3, 4 (G) | One-dimensional, Constant Potentials: The Potential Step | ||
| W Oct. 10 | Ch. 4 (G) | Flux & the 3D Continuity Eqn.; The Potential Step (cont.) | ||
| F Oct. 12 | Ch. 2 (GS); Ch. 4 (G) | The Potential Barrier; Tunneling | ||
| M Oct. 15 | Ch. 2 (GS); Ch. 4 (G) | The Finite Potential Well; Bound States | ||
| W Oct. 17 | Ch. 2 (GS); Ch. 4 (G) | Solving for Bound States in a Finite Well; The Delta-Function Potential | ||
| F Oct. 19 | Ch. 2(GS); Ch. 4 (G) | The Delta-Function Potential (cont.) | ||
| M Oct. 22 | Ch. 4 (G) | Multiple Delta-Function Pot'ls; On the Chemical Bond | ||
| W Oct. 24 | Ch. 2 (GS): Ch. 4 (G) | The S-Matrix; Quantum effect devices (STM's; RTD's) | ||
| F Oct. 26 | Ch. 2 (GS); Ch. 4 (G) | Transmission Resonances; The Harmonic Oscillator Potential | ||
| M Oct. 29 | Ch. 2 (GS); Ch. 4 (G) | The Harmonic Oscillator Potential (cont.) | ||
| W Oct. 31 | Ch. 2,3 (GS); Ch. 4, 5 (G) | The Harmonic Oscillator Potential (cont.); The General Structure of Quantum Mechanics | ||
| F Nov. 2 | Ch. 3 (GS); Ch. 5, 6 (G) | The General Structure of Quantum Mechanics (cont.); The Expansion Postulate Revisited (Closure) | ||
| M Nov. 5 | Ch. 3 (GS); Ch. 5, 6 (G) | The Set of Wave Functions as a Vector Space; Dirac Notation | ||
| W Nov. 7 | Ch. 3 (GS); Ch. 5, 6 (G) | Hermitian Operators; From psi(x) to |psi> and back again | ||
| F Nov. 9 | Ch. 3 (GS); Ch. 5, 6 (G) | The Uncertainty Principle and Ehrenhest's Theorem Revisited | ||
| M Nov. 12 | Ch. 3 (GS); Ch. 5, 6 (G) | Discrete and Continuous Bases; from psi(x) to psi(p) | ||
| W Nov. 14 | Ch. 3 (GS); Ch. 6 (G) | Operator Methods and the Harmonic Oscillator | ||
| F Nov. 16 | Away Trip: No Class | |||
| M Nov. 19 | Ch. 3 (GS); Ch. 6 (G) | Operator Methods and the Harmonic Oscillator (cont.) | ||
| W Nov. 21 | Thanksgiving Break | |||
| F Nov. 23 | Thanksgiving Break | |||
| M Nov. 26 | Ch. 3 (GS); Ch. 5, 6 (G) | The Matrix Structure of QM | ||
| W Nov. 28 | Ch. 4 (GS); Ch. 9, 7 (G) | Operator Methods and Angular Momentum | ||
| Th Nov. 29 | Ch. 3 (GS); Ch. 5,6 (G) | Degeneracy and Simultaneous Observables [Makeup] | ||
| F Nov. 30 | Ch. 4 (GS); Ch. 9, 7 (G) | Operator Methods (cont.); Spherical Harmonics | ||
| M Dec. 3 | Ch. 4 (GS); Ch. 7 (G) | Spherical Harmonics (cont.) | ||
| W Dec. 5 | Ch. 4 (GS); Ch. 7, 8 (G) | Sch. Eqn. in 3 Dim.; CM and relative coord. | ||
| F Dec. 7 | Ch. 4 (GS); Ch. 7, 8 (G) | Angular Momentum and the Central Pot'l Problem. | ||
| M Dec. 10 | Final Examination, CP 287, 9:30AM start time!!! | |||
Course Grades
Your grade will be determined in the following manner: problem sets (35%),
midterm exam (30%), final exam (35%).
The midterm exam will be a open required textbook exam (10/12/18: announced
that Gasiorowicz could be used as well) which you will be asked to work
in a single two-hour sitting. We will arrange an evening meeting time in
mid-October in order to conduct the exam.
[on 8/22/18 we determined the
date and time to be Monday, October 15, from 7-9 PM. Students who wish to do so
can work on it somewhat longer. I will reserve the room until 10PM.]
The final exam will be a in-class, open required textbook exam,
of three hours in
duration to begin at 9:30AM on M, Dec. 10 (if we can reserve an appropriate classroom -- otherwise it
will begin at 10:30AM, be two hours long, and held in CP 287).
You must pass the final examination in order to pass the class.
A significant portion of the course grade
is associated with the problem sets,
and rightly so. Working problem sets is necessary to develop
a genuine understanding of the material. You may discuss the problems
with others, and even collaborate, but you are required to write out
your solutions independently. The problem sets will be issued in
one-two week intervals, and late work (if no excusable reason exists)
will not be accepted. In the
event that our class is large, I reserve the right to institute
``die'' homework; that is, for each problem set, the homework problem(s)
that are actually graded will be determined by the roll of a die.
Note that complete problem set solutions will be available on
reserve in the Science library. I will also drop your
lowest homework score (in percent) in computing
your final homework grade.
Examples of excusable absences are
(University Senate Rules section 5.2.4.2 ):
It is good for you to discuss the course material with others, but
you really must perform all your course work *independently*.
You should write out your solutions by yourself, expressing your
solutions in your own words.
Cheating and plagiarism in tests or exams, indeed, in all aspects of
the course, are very serious academic offenses.
Violators of the academic code are subject to punishment
in accordance to University Senate Rules sections 6.3 and 6.4.
Course evaluations are an important and mandatory component of
our department's instructional
management system. The on-line course evaluation system
was developed to minimize the
loss of classroom time and to allow each student
ample time to evaluate each component of the
course and its associated instructor, providing
meaningful numeric scores and
detailed commentary.
To access the system during the spring evaluation window,
simply go to the Department of Physics & Astronomy web page,
click on the
link for Course Evaluations, and follow the instructions.
You will need to use your student ID# to log into the system; this
allows us to monitor who has filled out evaluations.
However, when you login you will be assigned a random number,
so that all you comments and scores will remain anonymous.
I will grant a homework problem's worth of credit to each of those who
fill out the online evalutions.
The percentage of total course points you earn will determine your grade in the course.
The following guidelines should help you interpret your
performance throughout the course of the semester.
Typically, a student who earns in excess
of 85% of the available points can expect to receive an ``A,'' whereas
a student who earns in excess
of 65%, but less than 85%, of the available points can expect to receive
a ``B.'' A student who earns in excess
of 45%, but less than 65%, of the available points
can expect to receive a ``C''. The following condition supercedes the
indicated guidelines. Irrespective of your total
earned points, in order to pass the class, you must
earn a passing grade on the final examination.
(i) Illness of the student or serious illness of a member of the
student's immediate family. Written verification required.
(ii) The death of a member of the student's immediate family. Written
verification required.
(iii) Trips for members of student organizations
sponsored by an academic unit, trips for University classes, and
trips for participation in intercollegiate athletic events.
(iv) Major religious
holidays. Students are responsible for notifying the instructor
in writing of anticipated absences due to their observance of
such holidays no later than the last day for adding a class.
For all excusable absences, when
feasible, the student must notify the instructor prior to the
occurrence of such absences, but in no case shall such notification
occur more than one week after the absence.
On-line Course Evaluation
This page was created by Susan Gardner and was last updated on August 22, 2018.