Course: PHY208

Instructor: Silviu Pufu

S 2018

### Description of Course Goals and Curriculum

The whole goal of this course is to understand where quantum mechanics came from and how we can use it to solve a variety of problems. This class focuses on time-independent and nonrelativistic quantum mechanics (because it's hard enough already without adding in relativity and time as a 4th dimension, and time-dependence is the main focus of Phy 305). It starts out with the double-slit experiment and interference, which leads us into how light exhibits both wave-and-particle-like properties. From this, we derive the “wave function” by looking at the probability of whether light will behave as a wave or a particle. The whole point of deriving this wave equation is that for rest of the course we will use it to solve a bunch of different problems, and understanding what it is and where it comes from is essential to obtaining a full understanding of each problem that we solve. From here, a bunch of mathematical tricks are taught and we learn how to manipulate the wave equation and analyze its probabilistic nature (mean/expectation, uncertainty, etc.). Once we have this solid foundation, we go into deriving the Schrodinger equation and then apply this equation to a slew of theoretical scenarios and different potentials. The Schrodinger equation is essentially just a differential equation that we have to solve for different conditions, and we solve it for a bunch: infinite box, finite box, delta potential, etc. Note that “solving” this equation is essentially finding the wave function that satisfies the conditions of the equation and finding the corresponding energies. We do this using math tricks that are learned along the way (like operators and commutators) and linear algebra. Once we have fully exhausted all of this analysis, or at least what is covered in the scope of this course, we moved on to analyzing the hydrogen atom, and learned about things like energy levels and rederived orbital states and energies from the quantum perspective (remember those from intro chem?), and finally angular momentum and electron spin.The whole goal of this course is to understand where quantum mechanics came from and how we can use it to solve a variety of problems. It starts out with the double-slit experiment and interference, which leads us into how light exhibits both wave-and-particle-like properties. From this, we derive the "wave function" by looking at the probability of whether light will behave as a wave or a particle. The whole point of deriving this wave equation is that for rest of the course we will use it to solve a bunch of different problems, and understanding what it is and where it comes from is essential to obtaining a full understanding of each problem that we solve. From here, a bunch of mathematical tricks are taught and we learn how to manipulate the wave equation and analyze its probabilistic nature (mean/expectation, uncertainty, etc.). Once we have this solid foundation, we go into deriving the Shrodinger equation and then apply this equation to a slew of theoretical scenarios and different potentials. The Shrodinger equation is essentially just a differential equation that we have to solve for different conditions, and we solve it for a bunch: infinite box, finite box, delta potential, etc. Note that "solving" this equation is essentially finding the wave function that satisfies the conditions of the equation and finding the corresponding energies. We do this using math tricks that are learned along the way (like operators and commutators) and linear algebra. Once we have fully exhausted all of this analysis, or at least what is covered in the scope of this course, we moved on to analyzing the hydrogen atom, and learned about things like energy levels and rederived orbital states and energies from the quantum perspective (remember those from intro chem?), and finally angular momentum and electrom spin.

### Learning From Classroom Instruction

Pufu's lectures are loaded with great info, examples, and explanations of complex topics. The best way to make sure you grasp everything covered in lecture is to just write down what Pufu is explaining during lecture, and then later on sit down with your notes, the notes Pufu posts online, and the textbook, and using all of those make sense of exactly what Pufu was saying and understand it in your own way. Pufu is a genius, so sometimes the way he understands and explains things is hard to initially grasp, but sitting down with the material following lecture allows you to make sure you really understand the material. In terms of what to do when you sit down, the best way to make sure you understand the material is to put everything in your own words. Synthesize the notes from class, the note handouts, and the book into a single description in your own words. Do this for each concept, whether it is a broad idea, like gaussian wave packet, or a specific idea, like a specific feature of a gaussian wave packet. Then, use this understanding to do a couple of the examples from any set of notes. Putting everything into your own words and understanding each step of the examples from class and the book is a great way to make sure you understand all of the material and will set you up to be able to figure out the problem sets.### Learning For and From Assignments

The problem sets are due weekly, and usually take around 10 hours or so. They're not overly difficult, with the exception of a couple problems throughout the year that definitely take a while, but making sure that you understand each problem is essential, as the problems are designed to complement the material and show you how to apply what was taught in class and in the book to solving a real problem. The problem sessions are great, as the TA's often are helpful in helping you make sense of some of the harder problems or confusingly-worded parts. Also, always work in a group- these problem sets would take way too long individually. Some of my friends could do it, but they were the exception instead of the rule. The best way that I found to do these sets was to learn the material and make sense of everything, and then try each problem on my own, but not spending a drastic amount of time if I got stuck on something. Then, I would meet up with the group and we would work through each problem, which helped me confirm or change what I had figured out on my own and learn how to do the parts I was stuck on. Working in a group also allowed me to see how other people approached these problems, which was often more clever than how I was going about them, which allowed me to better prepare for the time-crunched exams. Speaking of the exams, an amazing way to study for them was to go through the psets and explain how each problem was done in your own words since the psets were designed to help you understand the material. Sit down and go through each question, either redo it or write in your own words how it was done, and then write down the main topics that went into solving this problem.### External Resources

There are a lot of great lectures on specific topics from this course (MIT OpenCourseWare, Coursera, random youtube videos). Pufu does a great job explaining a lot of the physics concepts in class, but sometimes the math concepts are harder to understand, and these videos are a great way to get that extra explanation and understanding. Also, Pufu posts notes from another Princeton professor who taught the course when Pufu himself went here, Prof. Meyers. Meyers' notes are a great supplement to the lectures, as sometimes Meyers explains things a little more clearly in his notes than Pufu did in lecture, and vice versa for other topics. Other than that, the book is an invaluable resource, office hours are great, and the problem session is crucial for doing the assignments.### What Students Should Know About This Course For Purposes Of Course Selection

This course is required for physics majors and for the engineering physics certificate. It's a great introduction to quantum mechanics, which is often more easily learned in a classroom setting than from reading books. But to get the most out of this class it is essential that you put the time in to understand the concepts and complete the problem sets and understand these problem sets. This will give you a legitimate understanding of how quantum mechanics is currently constructed and analyzed, and really give you a new view on the world and in a lot of other stem classes. It's very well-taught and you know exactly what is expected of you. With all that being said, it is hard and it is a lot of time, so unless you are a physics major or pursuing the engineering physics certificate, really understand your motivation for taking this course because you need to make sure you want to put in the time to understand everything.Quantum Mechanics

The whole goal of this course is to understand where quantum mechanics came from and how we can use it to solve a variety of problems. It starts out with the double-slit experiment and interference, which leads us into how light exhibits both wave-and-particle-like properties. From this, we derive the “wave function” by looking at the probability of whether light will behave as a wave or a particle. The whole point of deriving this wave equation is that for rest of the course we will use it to solve a bunch of different problems, and understanding what it is and where it comes from is essential to obtaining a full understanding of each problem that we solve. From here, a bunch of mathematical tricks are taught and we learn how to manipulate the wave equation and analyze its probabilistic nature (mean/expectation, uncertainty, etc.). Once we have this solid foundation, we go into deriving the Shrodinger equation and then apply this equation to a slew of theoretical scenarios and different potentials. The Shrodinger equation is essentially just a differential equation that we have to solve for different conditions, and we solve it for a bunch: infinite box, finite box, delta potential, etc. Note that “solving” this equation is essentially finding the wave function that satisfies the conditions of the equation and finding the corresponding energies. We do this using math tricks that are learned along the way (like operators and commutators) and linear algebra. Once we have fully exhausted all of this analysis, or at least what is covered in the scope of this course, we moved on to analyzing the hydrogen atom, and learned about things like energy levels and rederived orbital states and energies from the quantum perspective (remember those from intro chem?), and finally angular momentum and electrom spin.