# Phys 3652 Spring 2024

# PHYS 3652 Quantum Mechanics - II (undergraduate)

### Vanderbilt University Spring 2024
Tu-Th 11-12:15 Stevenson 6638

### Office hours - M/Th - 2-3pm or by appointment

## Basic Information -

### Instructor : Prof. Raghav Kunnawalkam Elayavalli

### Pronouns : they/them

### Email : raghav.ke@vanderbilt.edu

### Office : Stevenson 6410

### Textbook : Griffiths Introduction to QM - second or third edition

### Website : https://www.raghavke.me/home/teachingtutorials/phys-3652-spring-2024 and on brightspace.vanderbilt.edu

### Prerecs : Quantum Mechanics - I PHYS 3651

## Introduction

The theory of quantum mechanics exists as a cornerstone of modern physics with many many extensions into nuclear particle physics. It is also the foundation to describing the mechanics of atomics and molecules and all fundamental particles. Quantum mechanics can be thought of as a generalization of classical mechanics where the particle-wave duality of matter reigns supreme. It is an enormously successful and practical physical theory, with predictions and experimental confirmations. The word quantum has greatly been abused in popular science and in the general consciousness with tangents into the nature of reality, what is measured and what is not etc… The math required to model quantum systems are inherently complicated but there is a more or less robust system to follow along to help you grasp some phenomenal concepts of reality.

## Learning Objectives

By the end of this course, you should be able to -

comprehend the wave functions of the hydrogen atom

solve problems involving addition of angular momentum

compute corrections to exact solutions of quantum systems using perturbation theory

explain the qualitative behavior of your solution to any problem

evaluate the reasonableness of solutions through such methods as dimensional analysis limiting/special cases, order of magnitude estimates, and verifying boundary conditions.

understand the connections with spectroscopy

apply symmetry principles to analyze the behavior of multiple-particle systems and periodic systems

reason the theory of scattering from simple assumptions

discuss the principles of radiation

connect what we learn in class and ongoing state-of-the-art research

## Syllabus and lesson plan

With our active learning approach towards QM, we will focus more on understanding the material via solving problems, either in homework or take-home exams. The course will be graded based on the following rubric

## Homework -

There will be a total of 6 homework problem sets related to the material we cover in class. Usually there will be at least 1 week gap between the homework is presented and when it is due, which means that sometimes the lecture material for the whole week or more is needed to solve the problems. You are encouraged to work together to solve problems but the solutions need to be written up individually, either clearly on paper or on latex and submitted before the due date. Your grades will be provided to you on brightspace (I assume) or via email privately before the next class along with the solutions. If there appears to be something consistent that I learn from your homework, we will discuss that in the following class.

## Midterm -

We will have a take-home midterm exam which I would expect that it should not take you more than 3 hours. This will be open book, open notes but just do not use the internet. If you have any other upper level quantum text book on hand like Landau and Lifshitz, Shankar or Sakurai, you are welcome to use those as well but it might possibly just take up more of your time and not be entirely useful. This exam should be done individually and the solutions will be provided the class following the mid-term.

## Final -

This is going to be a bit of a test case because it will be a group collaborative final. Since there are 10 of you in the class, we will form two groups of 5 students (you are free to choose) and solve the problems. In the end, I need one report from each group, detailing who did what, how the work was distributed and of course the solutions :). It will be a mixture of solving a problem on a paper, designing a realistic scenario about an experiment etc… You are free to use the course textbook and any notes you have in the class. If you need something technical like an integral or functions etc.. I will provide it to you. I will give a single grade for each report which means that all of you in one group will have the same grade for the final. This is to ensure that you are truly collaborative in spirit. I'm thinking we currently set aside 4 hours for this final, but lets see how the course progresses.

## Class participation -

At the start of each class, we will have someone recap what was done in the last class. I will call on you randomly but only twice during the entire course. During the class we will also have some time each class where you work with your peer and present what you have - this will be clearly discussed during each lecture so don't worry. This is the so called think-pair-share technique that we will try. All of this will count towards your grade in this sector.

## Additional problem set -

You must have noticed that the total points in the rubric add up to 110.. There will be one or two additional problem sets with 10 points total with challenging problems that require more time and thought. They can be primarily used as extra credit to help a grade. If you all as a class decide to work on them, that is also fine with me as long as it is clearly described who has done what.

## Grading for the course -

The course will be graded out of 100.

A (90, 100] A- (85, 90]

B+ (80, 85] B (75, 80] B- (70, 75]

C+ (65, 70] C (60, 65] C- (55, 60]

D+ (50, 55] D (45, 50] D- (40, 45]

Depending on how the course progresses, we can collectively take a decision where we are w.r.t a curve.

## Academic Integrity -

Listen, we all know that the solution sets for these homework problems from the text book are available somewhere on the Internet. You are taking an upper level physics course probably because you are interested in the material and find it exciting at some level or think it will be useful for you to study whatever you plan on doing next. I can discuss the topics and answer questions but ultimately, your learning is in your hands :) If you directly copy the homework from the internet or from your friends, you will have a very good homework score and frankly, even earn a good grade in the course. But, the information will not be retained and at the end, that is what is more important in this area. The concept of spin, emission spectra, perturbation theory, bells inequality etc.. are all phenomenally beautiful concepts and learning and trying to understand them is an amazing journey - one that I hope to provide in this semester. I am not going to go out of my way to check if someone is directly copying the homework etc and I'm going to assume good faith. I know it wont, but If a serious situation does arise, we will follow protocol within the department and if necessary, take it to the dean where the consequences are severe.

## Artificial Intelligence -

Generative Artificial Intelligence language models, such as ChatGPT, have become readily available and its been quite exciting and fun to play with them. However, they are not a replacement for your own thinking and comprehension. You will not master the concepts and skills in this course by relying on tools like ChatGPT to give you the answers.

The use of ChatGPT or other AI chatbots to give complete answers for any assignments in this course is prohibited. This does not mean that i will be checking it directly. To be very honest with you, the easiest way to see if a question has been solved by AI is the complete nonsensical nature of the answers... However, you may treat it like an expert colleague to hep resolve misunderstandings, provide additional examples or explanations, or other things that supplement the learning process. In these cases, you must provide an appropriate citation for the tools that you have used. If you have any doubt as to whether you are using an online learning support platform appropriately in this course, I encourage you to discuss your situation with me.

As a final word of caution, remember that these tools can be wrong (and often in subtle ways)! Engage with the feedback that they give you so that you weight it appropriately.

Read Vanderbilt's position on these tools here - https://www.vanderbilt.edu/brightspace/2023/08/16/guidance-on-ai-detection-and-why-were-disabling-turnitins-ai-detector/

## Accommodation -

This class respects and welcomes students of all backgrounds, identities, and abilities. If there are circumstances that make our learning environment and activities difficult, if you have medical information that you need to share with me, or if you need specific arrangements in case the building needs to be evacuated, please let me know. I am committed to creating an effective learning environment for all students, but I can only do so if you discuss your needs with me as early as possible. I promise to maintain the confidentiality of these discussions. If appropriate, also contact Student Access Services to get more information about specific accommodations.

Professional courtesy and sensitivity are especially important with respect to individuals and topics dealing with differences of race, culture, religion, politics, sexual orientation, gender, gender variance, and nationalities. Class rosters are provided to me as the instructor with the student’s legal name. I will gladly honor your request to address you by an alternate name or gender pronoun. Please advise me of this preference early in the semester so that I may make appropriate changes to my records.