Physics 316 – Introductory Quantum Mechanics Fall 2015 Instructor Dr. Joseph W. Howard - “Joe” Office/Phone: Henson Science Hall 305C, 410-548-5393 eMail: jwhoward@salisbury.edu Office Hours: MW 1:00 – 2:30pm ; T 10:00 – 11:00am ; F 1:00 – 2:00pm Class Hours: T/R 12:00 – 1:40pm, Henson Science Hall, Room 360 Textbook Required Text Introduction to Quantum Mechanics, 2nd Edition, Griffiths, David J., (Prentice Hall - 2005: ISBN 0-13-111892-7). Course Description, Objectives, & Policies Description This course is intended as an introduction to the principles and study of quantum mechanics. The exploration will include an investigation of wave mechanics, Schrödinger’s equation, Fourier techniques, operator formalism, eigenvectors and eigenvalues, one-dimensional potentials, correspondence and uncertainty principles, the harmonic oscillator, and the hydrogen atom. Emphasis will be placed on the development of problem solving skills through the application of the principles of quantum mechanics. Prerequisites: PHYS 309 (Math Physics), PHYS 313 (Modern Physics), & PHYS 314 (Mechanics). Course Goals 1. CONTINUE TO DEVELOP A GOOD FUNCTIONAL UNDERSTANDING OF PHYSICS The goal of physics is to understand the physical universe. An understanding of the subjects covered in the class will help prepare those of you who plan on a career that requires a thorough knowledge and understanding physics. Beyond that, an understanding of the physical principles may help you perceive the world around you in a more comprehensible, enjoyable, and fascinating way. 2. DEMONSTRATE AN ABILITY TO THINK CRITICALLY, LOGICALLY, & ANALYTICALLY WHEN SOLVING PROBLEMS In order to solve a problem, you must critically examine the information available in a given situation; determine an effective method to approach the problem, and carry through to the solution, including a critical examination of the final answer to see if it is reasonable. To understand a physical situation and to solve physics problems requires the ability to use mathematical expressions that are solvable and that represent the situation. Students should be able to see the linkage between the math used to that of the physical principles involved. These skills are not only essential to solving problems in physics, but to solving problems in general, and are applicable to many situations in many different environments. 3. UNDERSTAND FUNDAMENTAL PRINCIPLES OF QUANTUM MECHANICS Quantum mechanics has had enormous success in explaining many perplexing features of the physical world on the smallest scales. Quantum theory generalizes all classical theories, including mechanics, electromagnetism, and provides accurate descriptions for many phenomena such as blackbody radiation and stable electron orbits within atoms. There are many topics to cover when exploring the fascinating realm of quantum mechanics but in doing so a new interpretation and process for describing the natural world is developed. 4. DEVELOP A CONCEPTUAL & COMPUTATIONAL UNDERSTANDING OF THE SCHRÖDINGER EQUATION Schrödinger’s equation is the name of the basic non-relativistic wave equation used in quantum mechanics to describe the space & time dependence and behavior of a particle in a field of force. There is the time dependant equation used for describing progressive waves, applicable to the motion of free particles. And the time independent form of this equation used for describing standing waves. The Schrödinger equation plays the role of Newton’s Laws of motion and energy conservation rules in classical mechanics (the motion of macroscopic objects) in that it is used to predict the future behavior of a dynamic system. It is a wave equation in terms of the wavefunction which predicts analytically the probability of events or outcomes. Schrödinger's equation describes the wave like properties of matter and was one of greatest achievements of 20th century science so it will be necessary to understand the equation and how to apply it to certain situations. 5. BECOME SKILLED IN APPLICATIONS OF QUANTUM MECHANICAL TECHNIQUES You will explore how quantum mechanics is used in describing situations like the infinite and finite energy potentials, the harmonic oscillator, free particles, three dimensional systems, the formal mathematical quantum theory of the hydrogen atom, angular momentum, and spin. You will, along the way, develop a quantum theory formalism that describes the state of a system using its wave function, and the system’s observables, by employing operators to extract information given certain boundary conditions. What are function spaces, eigenvalues, and the uncertainty principle? Policies Attendance: Attendance is required. You must notify the instructor in advance if you are unable to attend a class period. Cell Phones: Please turn off your cell phones (or select a silent ring) during the class lecture. You may not talk or text on the phones in the classroom during lecture. Writing Requirement: Homework assignments and exam problems will require a written response. These responses must be grammatically correct with proper spelling and punctuation. Students with Disabilities: Any student in this course who has a disability that may prevent him or her from fully demonstrating his or her abilities should contact me personally as soon as possible so that we can discuss accommodations necessary to ensure full participation in this class and facilitate educational opportunities. Academic Integrity: Academic integrity is at the heart of education because there is no doubt that honor and the quest for knowledge are inexorably intertwined. Salisbury University is an academic community dedicated to the achievement of intellectual growth where the pursuit of freely exchanged ideas and active study is an essential element of academic excellence and development. Students and faculty are expected to meet the highest possible standards of personal, ethical, and moral academic conduct. These standards require personal integrity, a commitment to honesty without compromise, as well as truth without equivocation. Academic trust means respecting these truths and principles, without which no university can exist. Academic Dishonesty: This instructor adheres to the policy of academic dishonesty as it appears in the college catalog and outlined in the student handbook. Course Philosophy This is a physics class and, therefore, it has similarities to all other physics classes. Quantum mechanics is the best-confirmed theory of particle dynamics in existence today. Not only is it the basis for all digital technologies, it also serves as the theoretical foundation for our bestconfirmed theories of matter (quantum field theories). However, philosophically, there is no current consensus on just how to interpret it: The theories used to explain quantum mechanics are conceptually complex, highly mathematical at times, and somewhat philosophical in nature and will require a great deal of effort to build a beginning understanding of the subject. Many in the field often say, “no one really understands quantum theory, they just know how to use it.” The meaning of quantum theory is a bit of a taboo subject, but it is hotly debated, and everyone thinks about it, and those that truly try to understand it are also shocked by quantum theory’s implications. Some students believe that if they can follow the lectures in class, then they have learned all they need to know about quantum mechanics. This is not true. A student must do a significant amount of work outside of class thinking about, and interacting with, the course material. No one ever learns physics by simply reading about it or listening to someone talk about it. You learn it by making the effort to understand the material, building mental pictures, and by solving problems using the principles learned. The standard requirement in a college class is that you spend two hours outside class working on the material for every hour in class. Since this is a three-hour class, you should plan on spending at least six hours per week outside of class interacting with the material and solving problems. Few students will be able to succeed in this class without investing more than that amount of time. As stated earlier, you can only learn by personally interacting with the material and solving problems. Consequently, I emphasize three methods of learning in this class: 1. Reading and thinking about the assigned material before it is discussed in class. 2. Solving problems using the physics concepts and principles. 3. Discussing the material and solving problems in class, including working with your classmates. Thinking about problems and solving them on a regular basis will allow you to learn and appreciate the subject matter in a natural way, without having to cram everything at the last moment. I want you to enjoy Physics 316. The material we will be covering is fascinating and applicable. In order to make this class as interesting and useful as possible, I will need to get feedback from you. Please feel free to ask questions in class and to come by my office during office hours. Course Structure & Assignments The course will be divided into four modules and may consist of the following graded assignments: 1. Class Activities 2. Homework Problems 3. Midterm Exam or Final During each module, I will distribute detailed descriptions of the material and homework problems assigned. A calendar listing the tentative dates for course subject material is attached as the last page of this syllabus. The calendar may be revised at the discretion of the professor. Homework Homework will consist of problems assigned mostly from the text. Homework will be due by 5:00 p.m. on the date specified. It may be turned in during lecture or deposited in the box outside my office. Here are some suggestions for the homework assignments: Read the problems as soon as you get them. You don’t have to spend any time working on them; just think about them as you read and study the material. Don’t procrastinate!! You will have at least a week to work on the problems. Don’t wait until the last minute to do them. In particular, you will have an opportunity to ask questions in class to help you further understand the problems. Ask Questions!! If you are having problems with the homework, seek help!! You may discuss the problems with your classmates as well as with me during office hours. Although you may discuss the homework with your classmates, all work handed in must be your own. Copying another person’s work is plagiarism, and will be considered cheating. I encourage you to talk with others in order for you to get a general understanding of the work. However, each person must work out detailed solutions of the problems individually. Doing the homework is the best way to prepare for the exams since test questions will be similar to problems assigned for homework. Class Activities You will be expected to ask and answer questions and to participate actively in the class and during in-class activities. You are also expected to actively collaborate in group problem-solving sessions in the class and/or to present homework solution ideas to the entire class. Active Participation: Because learning requires active participation, and not just passive listening, we will be doing various activities in the classroom that involve student participation. These activities will help the student learn and give the instructor valuable feedback on how well the students have mastered the course material. Group Work: Occasionally, classroom groups may be created during the semester. The groups will allow you to work together with your peers to understand the material. Group activities will include discussion of homework, as well as working on other problems designed to help you understand the material. All activities in the groups will be cooperative, not competitive. A good group member is not necessarily one who knows the answers. A good group member is one who comes prepared and regularly participates in the work, enters into the spirit of trying to help his or her fellow group members answer questions, work problems, and better understand the material. Exams & Final There will be three mid-semester exams. The final will be comprehensive, covering material from the entire semester. The best preparation for these tests is a thorough understanding of the material and an understanding of the problems done for homework. Grading 3 Midterm Exams (3 x 15%) Homework Assignments Class Activities Final Comprehensive Exam 45% 34% 5% 16% ------ Total = 100% ** Grade Scale: The following criteria will be used for determining letter grades: 90 -100% = A: Superior Work. Student demonstrates a thorough and complete understanding of the subject. 80 - 89% = B: Excellent Work. Student demonstrates an above average understanding of the subject. 70 - 79% = C: Good Work. Student demonstrates an average understanding of the material. 60 - 69% = D: Fair Work. Student demonstrates below average understanding of the material and has completed most of assignments. 0 - 59% = F: Unsatisfactory Work. Student does not demonstrate and adequate understanding of the subject and has not turned in all assignments. Grades of A and B are given to students who have demonstrated by their performance on exams, homework and in class exercises that they not only can do the required problems, but that they also understand the material well enough to explain it to others and to engage in knowledgeable conversations about the principles and meaning of Quantum Mechanics. Such students will have NOT have memorized and regurgitated course material. They will have retained the course material because they have spent the time to become familiar with it and have gained some understanding of it. A and B students will have devoted the required time and effort to the course. It is generally accepted that each week successful students should spend a minimum of 2 to 3 productive hours outside of class for each hour in class. This course will require an investment each week of 8 to 12 productive hours outside of class studying the previous class material, doing homework, preparing for the next class and studying for exams. Inclement Weather In case of inclement weather, call the Gull Line at 410-546-6426 for weather related closing information or check the Salisbury University web page. Important Notice If your Physics 316 grade will affect any of the following: 1) whether you receive or retain a scholarship (athletic or otherwise); 2) your eligibility to participate in any university sponsored activity; 3) your standing with your fraternity, sorority, the university, or any other student organization; NOW IS THE TIME TO BECOME CONCERNED - NOT AT FINAL EXAM OR AFTER FINAL GRADES HAVE BEEN DETERMINED!! Please do not wait until the last minute, when it will be too late for anyone to help you! Also remember, we are here to learn knowledge and most of all have FUN!! (May da 4s b w/u!) Physics 316 – Quantum Mechanics – Fall 2015 Tentative Schedule Dates Sep. 1 – Oct. 1 October 1 Oct. 1 – Nov. 5 November 5 Nov. 5 – Dec. 3 December 3 Dec. 3 – Dec. 10 Concepts Selected From Chapters Wave Functions One Time-Independent Schrödinger Equation (Stationary States, Infinite Square Well, Harmonic Oscillator) Two Exam One Time-Independent Schrödinger Equation (Free Particle, Delta Function, Finite Square Well, Applications) Formalism (Hilbert Space, Observables, Hermitian Operators) Two Three Exam Two Formalism (Uncertainty Principle, Dirac Notation) Three Schrödinger Equation in Three Dimensions (Spherical Coordinates, Hydrogen Atom) Four Exam Three Schrödinger Equation in Three Dimensions (Angular Momentum, Spin) Identical Particles (Two particle systems, atoms, solids, statistical quanta) Four Five Detailed schedules will be provided during the semester. Final Exam is Scheduled for Thursday, Dec. 17th, 10:45am – 1:15pm