Lecture 5 Operators and Schrodinger Equation University Physics

Lecture 5 Operators and Schrodinger Equation University Physics: Mechanics Iksan Bukhori, M. Phil iksan. bukhori@president. ac. id 2019

Textbook and Syllabus Textbook: “Physics for Scientists and Engineers”, Serway and Jewett 9 th Edition Syllabus: (tentative) Week 1 -3: Intro to Quantum Physics Week 4 -6: Quantum Mechanics Week 8 -10: Atomic Physics Week 11 -13: Particle Physics and Cosmology Iksan Bukhori Quantum Physics 1/2

Grade Policy Grade Point: 85 – 100 70 – 84 60 – 69 55 – 59 0 – 54 : A : B : C : D : E (GPA = 4) (GPA = 3) (GPA = 2) (GPA = 1) (GPA = 0) § The use of smartphone calculator in quizzes and exams is prohibited. Iksan Bukhori Quantum Physics 1/3

Grade Policy Grades: Final Grade = 10% Homeworks + 20% Quizzes + 30% Midterm Exam + 40% Final Exam + Extra Points § Homeworks will be given in fairly regular basis. The average of homework grades contributes 10% of final grade. § Homeworks are to be written on A 4 papers, otherwise they will not be graded. § Homeworks must be submitted on time, on the scheduled day of the lecture. If you submit late, the penalty will be – 10·n points, where n is the total number of lateness made. § There will be 2 quizzes. The average of quiz grades contributes 20% of final grade. § Midterm and final exam schedule will be announced in time. Iksan Bukhori Quantum Physics 1/4

Grade Policy § Extra points will be given if you solve a problem in front of the class. You will earn 1, 2, or 3 points. § Make up of quizzes and exams will be held within one week after the schedule of the respective quizzes and exams. § To maintain the integrity, the maximum score of a make up quiz or exam can be set to 90. Basic Physics 1 Homework 6 Rudi Bravo 009201700008 21 March 2021 No. 1. Answer: . . . . Heading of Homework Papers (Required) Iksan Bukhori Quantum Physics 1/5

Lecture Activities § Lectures will be held in the form of Power. Point presentations. § You are expected to write a note along the lectures to record your own conclusions or materials which are not covered by the lecture slides. How to get good grades in this class? • Do the homeworks by yourself • Solve problems in front of the class • Take time to learn at home • Ask questions Iksan Bukhori Quantum Physics 1/6

Lecture Material § Latest lecture slides will be uploaded to my blog iksanbukhori@wordpress. com § You are responsible to read and understand the lecture slides. I am responsible to answer your questions. § Quizzes, midterm exam, and final exam will be open-cheat sheets. Be sure to have your own copy of lecture slides. You are not allowed to borrow or lend anything during quizzes or exams. § But: A homework can be submitted late without penalty if a scanned or photographed version of the homework is sent to iksan. bukhori@president. ac. id before the class begins. Iksan Bukhori Quantum Physics 1/7

Extra Assignments § There will be no remedial for any quizzes nor exams. § As replacement, you may submit a neat summary of your notes or collection of problems and solutions related to all topics covered up to that point in handwritten with A 4 paper § This extra assignment will not be announced beforehand has to be submitted one day after your quiz/exams paper is returned § The extra grade depends on the materials covered, how neat it is and how good your understanding of the materials actually is (Copying my slides or the book(s) will not do) Iksan Bukhori Quantum Physics 1/8

Postulates of Quantum Physics Iksan Bukhori Quantum Physics 1/9

Operators Examples: 1. Linear 2. Linear 3. Not Linear 4. Not Linear Iksan Bukhori Quantum Physics 1/10

Review: Eigenvalues and Eigenfunctions Iksan Bukhori Quantum Physics 1/11

Back to Postulate of QM 4. To every observable quantity, there exists an operator associated with it. For example, momentum operator is given by Position operator is given by And energy operator is given by For every operator, the general form of the expectation value of the corresponding observable is given by and Iksan Bukhori Quantum Physics 1/12

Commmutativity of Operator Like matrix multiplication, the order of operator matters. While To measure the importance of order of operator, there is a quantity called commutator defined as For example, Iksan Bukhori Quantum Physics 1/13

The Collapse of Wave Function Iksan Bukhori Quantum Physics 1/14

The Collapse of Wave Function Iksan Bukhori Quantum Physics 1/15

Math Interlude: Fourier Transform Position Space Momentum Space Iksan Bukhori Quantum Physics 1/16

Collapse of wave function Iksan Bukhori Quantum Physics 1/17

Schrodinger Equation It describes how wave function evolves over time Where Iksan Bukhori Quantum Physics 1/18