NORTH CAROLINA AGRICULTURAL AND TECHNICAL STATE UNIVERSITY

Course Syllabus Course Information Course Number/Section Course Title

PHYS 420-01 Quantum Mechanics I

Term Days & Times

Fall- 14 TR- 11:00-12:15

Professor Contact Information Professor Solomon Bililign Office Phone 336-285-2328 Other Phone 336-334-7424 (Lab) Email Adresse [email protected] Office Location Marteena 306/Gibbs 302 Office Hours TR 8-11 am, W -all day Other Information You can make appointments if you cannot make it during the office hours Course Pre-requisites, Co-requisites, and/or Other Restrictions Phys 406, Phys 405 A course in the Mathematical Methods of Physics would be a distinct advantage, though not an absolute pre-requisite. Course Description

This course presents a mathematical introduction required for the understanding of quantum mechanics. The solutions of the Schrodinger equation for a free particle and a particle in one-dimensional potentials (square, barrier, etc.), and the postulates of quantum mechanics are presented. The simple harmonic oscillator problem is solved. Other topics include angular momentum, spin, the two-particle problem and the hydrogen atom. Prerequisites: PHYS 405 and PHYS 406. (F;S) Student Learning Objectives/Outcomes

Quantum mechanics is, like most modern theories, is a theory which makes predictions about physical events, but does not actually contain a component which attempts to describe “the why”. The merit of such a theory is judged solely by its agreement with experiment for observable, physical values. In this respect, quantum mechanics has achieved unparalleled success in predicting events classical mechanics cannot. At the conclusion of the course a student must be familiar be able to

2

1. Develop the physical principles and the mathematical background important to quantum mechanical descriptions. 2. Summarize experiments and theories formulated during the early decade of the century. These observations and theories comprise the genesis of quantum mechanics. 3. Establish the mathematical properties of the waves that describe free particles 4. Consider the effect of external force acting on a quantum mechanical particle. The force is assumed derivable from some potential energy V(x). We will solve the Schrodinger equation for different potentials. These include step potentials one dimensional barrier problems, infinite and finite potential wells. 4. Understand the basic postulates of quantum mechanics which serve to formalize the rules of quantum mechanics. Mathematical concepts materials to these postulates are developed along with the physics. 5. Understand the significance of constants of motion, and see their relation to fundamental symmetries in nature 6. Solve the harmonic oscillator Schrodinger equation, and consider some applications of the harmonic oscillator The following learning objectives are accomplished through this course. Objective 1: Effectively use information technology to find, interpret, evaluate, and use information discerningly. Outcome: Students will demonstrate the ability to use information technology tools to conduct literature survey, and do research Objective 3: Effectively employs critical thinking skills in written and oral communication. Outcome: Students will demonstrate the ability to employ critical thinking in solving problems which are very complicated and mathematically challenging Objective 4: Effectively relate ideas and concepts, as well as modes of inquiry, across disciplines Outcome: Students will demonstrate the ability to relate ideas and concepts from physics to chemistry, materials science and engineering Objective 5: Use analytical thinking skills to evaluate information critically. Outcome: Students will demonstrate the ability to use analytical thinking skills to evaluate the content of the course as it applies to real life problems and modern technology. Objective 6: Apply multiple modes of inquiry, including quantitative and qualitative analysis, to formulate, describe, evaluate, and solve problems Outcome: Students will demonstrate the ability to apply multiple modes of inquiry, including quantitative analysis, to formulate, describe, evaluate, and solve problems. Objective 7: Apply scientific reasoning skills to model natural, physical, social, and aesthetic phenomena using multiple modes of inquiry: Outcome: Students will develop to use quantum theory to model natural and physical phenomena in materials science, chemistry and nanotechnology. Objective 8: Use a wide range of disparate information and knowledge to draw inferences, test hypotheses, and make decisions. Outcome: Students will demonstrate the ability to Use a wide range of disparate information and knowledge to draw inferences, test hypotheses, and make decisions in research be able to apply this theory to other applied areas like nuclear physics, atomic and molecular physics, laser physics etc.

Course Syllabus

Page 2

3 Required Textbooks and Materials Required Texts Introduction to Quantum Mechanics, 2nd Edition David Griffiths Suggested course reference books

Introductory Quantum Mechanics: 2nd edition By Richard L. Liboff Addison-Wesley Publishing Company, 1992. Understanding Quantum Mechanics By M. A. Morrison. Prentice Hall, 1990. Assignments & Academic Calendar Topics, Reading and problems to work on Assignments, Due Dates, Exam Dates (optional: withdrawal dates, holidays, etc.) additional problems will be assigned after every lecture and are due the next class. Lecture 1 1

Date 8/20

Topics Mathematical Introduction- Linear Vector Spaces, Representations, Linear Independence, Bases Mathematical IntroductionInner Product Spaces Dual Spaces Inner Product Theorems Gram-Schmidt Orthogonalization Subspaces Linear transformation, metrics Linear Operators, The Eigenvalue-Eigenvector Problem,

Quiz

2

8/25

3 4

8/27 9/1

5

9/3

Review of Modern Physics Black Body Radiation, Photoelectric Effect Bohr’s Model, Waves vs Particles The wave function, The Schrodinger equation, Statistical interpretation, and probability: 1.1-1.3

Quiz 4

6

9/8

7

9/10

Normalization, Momentum Uncertainty Principle 1.41.6

Quiz 6

8

9/15

Time independent Schrodinger equation-Stationary States, Infinite square well-2.1-2.2 Exam 1

Quiz 7

9/17

Quiz 1

Quiz 2 Quiz 3

Quiz 5

9

9/22

Schrodinger Equation with Potential- Infinite square well. 2.2

Quiz 8

10

9/24

Harmonic Oscillator-2.3

Quiz 9

11

9/29

Quiz 10

12 13

10/1 10/6

Harmonic Oscillator-2.3 Free particle 2.4 The Delta Function Potential-2.5

14

10/8

Quiz 13

15

10/15 10/20

Solving The TISE for Piecewise Constant Potentials. Notes Exam 2 The Finite Square Well-2.6

Quiz 14

16

10/22

Formalism Hilbert space, observables-3.1-3.2

Quiz 15

Course Syllabus

Quiz 11 Quiz 12

Page 3

4 17

10/27

Eigen functions of a Hermitian Operator-3.3

Quiz 16

18 19 20 21 22 23 24

10/29 11/3 11/5 11/10 11/12 11/17 11/19 11/24 12/1 12/3

Generalized Statistical Interpretation-3.4 The Uncertainty Principle 3.5 Dirac Notation: 3.6 More on Formalism Schrodinger equation in Spherical Coordinates -4.1 Schrodinger equation in Spherical Coordinates-4.1 The Hydrogen Atom-4.2 Exam 3 The Hydrogen Atom-4.2 Angular Momentum-4.3 comprehensive

Quiz 17 Quiz 18 Quiz 19 Quiz 20 Quiz 21 Quiz 22 Quiz 23

25 26

FINAL EXAM

Quiz 24 Quiz 25

Grading Policy Homework: Quizzes daily- Part a in the quiz is to test if you have read the material before coming to class. It is easy and usually multiple-choice conceptual questions that will be 10 minutes long. Part b is to be done at the end of the class. You will start working on it and should be turned in by the end of the day. These are problems based on the lecture of the day. You are encouraged to solve the problems in the book. Solutions are available on line so you can practice and learn how to solve them. . Exams:

There will be three exams. The exams schedules will be announced as the course proceeds.

Grading:

quizzes Three Exams 12% each Final Exam

44% 36% 20%

Grade Scale

Course Policies

Course Syllabus

Page 4

5 Make-up exams Make up exams are given only with valid excuses Extra Credit Attendance of all departmental seminars is a requirement and students will earn extra credit. Late Work No late work is accepted Class Attendance

A student is not allowed to miss a class without reasonable excuse and justification. Classroom Citizenship Civility and good conduct is expected. Coming on time and turning off all cell phones, and waiting until the class ends are expected of each student. Technical Support If you experience any problems with your A&T account you may call Aggie Tech Support (formerly Help Desk) at 336.334.7195.

Field Trip Policies / Off-Campus Instruction and Course Activities Student Affairs website http://www.ncat.edu/~staffair/; Student Handbook: http://www.ncat.edu/~deanofst/Handbook.htm; Student Travel Procedures and Student Travel Activity Waiver http://businessfinance.ncat.edu/policies%20and%20procedures%20index.htm

Off-campus, out-of-state, and foreign instruction and activities are subject to state law and University policies and procedures regarding travel and risk-related activities. Information regarding these rules and regulations may be found at the website address: Student Travel

Procedures and Student Travel Activity Waiver http://businessfinance.ncat.edu/policies%20and%20procedures%20index.htm. Additional information is available from the office of Student Affairs, please check the website at http://www.ncat.edu/~staffair/. Below is a description of any travel and/or risk-related activity associated with this course.

Other Policies (e.g., copyright guidelines, confidentiality, etc.) Student Handbook: http://www.ncat.edu/~deanofst/Handbook.htm Family Educational Rights and Privacy Act http://www.ncat.edu/~registra/ferpa_info/index.htm Student Conduct & Discipline North Carolina A&T State University has rules and regulations that govern student conduct and discipline meant to ensure the orderly and efficient conduct of the educational enterprise. It is the responsibility of each student to be knowledgeable about these rules and regulations. Please consult the undergraduate http://www.ncat.edu/~acdaffrs/Bulletin_2008-2010/2008-2010_Undergraduate_Bulletin.pdf and graduate bulletins: 2008-2010 Graduate Catalog.doc http://www.ncat.edu/~gradsch/cstudents.html and student handbook http://www.ncat.edu/~deanofst/Handbook.htm for detailed information about specific policies such as academic dishonesty, cell phones, change of grade, disability services, disruptive

Course Syllabus

Page 5

6 behavior, general class attendance, grade appeal, incomplete grades, make up work, student grievance procedures, withdrawal, etc.

Compliance with the Americans with Disabilities Act North Carolina A&T State University is committed to complying with the Americans with Disabilities Act of 1990 and Section 504 of the Rehabilitation Act of 1973 by providing equal access to the programs, services and benefits to qualified students with disabilities. All reasonable efforts will be made to accommodate the needs of students with documented disabilities. If you have a disability that requires an accommodation during the semester, please REGISTER with the Office of Veterans and Disability Service (OVDSS) located on campus in Murphy Hall (334-7765). Make sure that you notify OVDSS of any disability accommodation requests prior to the start of classes or within the first two weeks of classes. These descriptions and timelines are subject to change at the discretion of the Professor. 01.27.09 – Submitted to Faculty Senate by LEW

Course Syllabus

Page 6