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What are the prerequisites for basic quantum mechaics

  1. Nov 4, 2015 #1
    Hello everyone, I'm currently a high school student that hopes to be a physicist one day and I'm part of a special science and math focused program in a public high school, which was started to promote STEM. It's a relatively prestigious and very rigorous program with a full on research project in senior year where the students collaborate with scientists nearby (the school is located near a military lab), and this is obviously going to help a great deal with getting into college. Because of how accelerated the program is, there is a lot of choices for me to make on what STEM classes I take, with many being exclusive to the program and all being modified in some way for the program. Because of this and the fact that I want to be a physicist I was wondering if it would be feasible for me to independently study *basic* quantum mechanics in my senior year (independent study is available in certain situations, and if I was able to accomplish this I'm relatively certain that I would be allowed to do so).

    I'm not the most familiar with the progression one would take to get up to the level of quantum mechanics, but the way I understand it with Calculus under my belt it would be enough math for me to understand the very basic ideas of it (again, this is not from an actual physicist or student, so please do correct me if I'm wrong). To give you an idea of my situation, the math and science progression that I go through during my time in high school is:
    9th grade: Algebra 2 for math, AP Environmental Science and Biology
    10th grade: Trig and Precalc, AP Statistics, AP computer science (counts as a math class), Chemistry
    11th grade: AP Calculus AB, AP Physics C: Mechanics, possibly AP Chemistry
    12th grade: AP Calculus BC, a semester of basic Linear Algebra, AP Physics C: Electricity and Magnetism

    So what does everyone think? Would I be able to learn enough basic QM through independent study with the things under my belt shown above that it would be worth it to dedicate a semester or even the whole year to it? Any and all input is appreciated, and if I could learn a significant amount of physics what introductory textbooks would you recommend that I could understand with the level of knowledge that I would have during my senior year?
     
  2. jcsd
  3. Nov 4, 2015 #2
    A good background in Calculus and Linear Algebra is really all that's needed in my opinion. And learning quantum mechanics actually helped my understand linear algebra a bit better.
     
  4. Nov 4, 2015 #3
    In my opinion, the boock Zettili
    Quantum Mechanics: Concepts and Applications, 2nd Edition

    is a bock that start from basic concept mathematics and physics, is ideal for some man that do not a complete physics formation..
     
    Last edited by a moderator: Nov 5, 2015
  5. Nov 5, 2015 #4

    PeroK

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    I'm learning QM at the moment. I've got David Griffiths "Introduction to QM". I'd say it's highly mathematical. You need Complex Numbers for a start, lots of integration, differential equations and, of course, Linear Algebra.

    I'm not sure what "basic" QM is. In QM, even studying a free particle leads to mathematical complexities. I suggest that any serious study would eat up your time. It would be a challenge, in any case. It's up to you whether you take it on, but I would say that if you do and you just bounce off it (if there is simply too much new maths to learn), then I wouldn't worry about it.

    You might also ask whether it's a good idea to jump into QM before you've studied Classical Mechanics.
     
  6. Nov 5, 2015 #5
    We used this book in my 2nd year studies of Quantum Mechanics, however pretty much everyone in the class disliked it. In 3rd year we used:
    http://www.pearsonhighered.com/educator/product/Quantum-Mechanics/9780321765796.page
    Everyone much preferred this as Griffiths uses little to no linear algebra, while McIntyre bases, bras and kets, before going wavefunctions as differential equations.
     
  7. Nov 5, 2015 #6

    jtbell

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    For basic quantum mechanics as presented in an "introductory modern physics" textbook such as Beiser or Serway/Moses/Moyer (there are several others), you need only some classical physics (energy, momentum and some basic electromagnetism, mainly), and differential and integral calculus. They generally introduce other math concepts as needed from linear algebra, differential equations, etc.

    At many or most colleges and universities in the US, students get their first exposure to QM from one of these books, then move on to Griffiths and similar books in a later course.
     
  8. Nov 5, 2015 #7
    plus one on ogg's advice.

    More good advice from PeroK.

    As far as "bouncing off it," take a look at the Wiki page on Schrodinger Equation:
    https://en.wikipedia.org/wiki/Schrödinger_equation
    If your eyes glaze over trying to read through that, then don't worry about it. There's plenty of very interesting basic physics to learn before you get to QM.
     
  9. Nov 5, 2015 #8
    Thanks so much for the input, everyone! It seems the majority of people are saying that I could learn the basics out of a textbook, but now the question seems to be more, as ogg said, if it's worth it. How much exactly would I be able to learn with that level of knowledge? Would it keep me busy for a semester, a year, etc?

    Also, as a side note directed towards PeroK, I will have studied basic mechanics in AP Physics C: Mechanics by the time I do this. Do you think this class would cover the basics to a good enough extent where I could follow one of the textbooks the others have recommended?
     
  10. Nov 6, 2015 #9

    PeroK

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    I'm not familiar with that course, but somes topics to cover before QM might be:

    Simple Harmonic Motion
    Energy, Potential, Conservative Forces
    Angular Momentum
    Lagrangian/Hamiltonian mechanics

    Something like Lagrangian mechanics would be tough, if you want a challenge. It might only take a few days, but it should stretch you conceptually and mathematically.

    And studying Angular Momentum should be a good test of your capabilities at this stage.
     
  11. Nov 7, 2015 #10
    Thanks a bunch for the suggestions! I'll make sure I understand those before I move on to QM, if I do decide to study it. I myself have not taken these classes yet, so I don't know if these topics are covered either. If they aren't, I'll make sure I spend however long I need to independently catching up before I move to QM. Thanks again for all of your help, everyone!
     
  12. Nov 7, 2015 #11
    In my opinion, to study quantum mechanics successfully, all one needs is basic linear algebra, differential equations, and introductory physics (E&M/Mechanics).

    However, to UNDERSTAND quantum mechanics requires much more. As for what that means in terms of prerequisites, I cannot say as I still do not understand quantum mechanics...
     
  13. Nov 9, 2015 #12
    It is hard to know what is meant by basic quantum mechanics. In my undergraduate college, we did not get to QM until the last semester of our Jr year. (I got it one semester earlier through a chemistry curriculum through a course called Physical Chemistry). My Freshman chemistry course had many QM ideas introduced.

    By my 2nd semester Jr year we physics majors had : Analysis (Calculus 2 semesters), Linear Algebra, Differential Equations, and Real Analysis. We were concurrently taking courses in partial differential equations and Complex variables. We had two years of classical physics and upper undergraduate courses in Classical Mechanics and Electromagnetics 1.

    Even with all that preparation, QM at the undergraduate level (in those days we used Merzbacher), offered challenges.
    I disagree with some of the members of the thread that linear algebra, differential equations and introductory physics is sufficient. After all Schrodinger's equation is a complex partial differential equation (often solved by separation of variables in textbooks problems). Hard to address this without a course in partial differential equations. Moreover, it is hard to see no matter how basic that QM gets it would not use Schrodinger's equation. If it uses Heisenberg representation, it is even worse.

    It is great that you have the opportunity to study with professors and subject matter experts perhaps in military labs. My experience with these professionals is they had varied research and applied areas.

    Classical Mechanics: Tides, Earth's gravity, Rocket trajectories, Inertial Guidance Systems, Optimal Control and Filtering. Satellite Tracking and GPS

    Electromagnetics and Plasmas: Energy transfer, Lasers

    Quantum Mechanics: Invisibility, Quantum Information, psbly Cryptography, Lasers

    Some of the best experts were so good and engaging in their research areas that I got involved in Classical Mechanics rather than my idea of using QM, and I never looked back. Do not be surprised if your direction is changed by an excellent teacher.
     
  14. Nov 9, 2015 #13
    Thank you very much for that reply! It was very insightful and offered a different perspective from what most others have said. Luckily I have more than enough time to decide if I will pursue independent study or not (right now I'm looking at textbooks for a class offered in some Universities called Quantum and Thermal Physics, which is taken in the freshman year and is apparently more an introduction to these topics with a little less math involved, especially focusing on thermal physics), and from this reply it looks like I'll most likely be taking the traditional route taking one semester electives rather than independent study. Who knows, maybe if this class I'm looking at is worth studying and not to math intensive I'll independent study for a semester and take an elective for the other semester. Thanks again for your and everyone else's help!
     
  15. Nov 10, 2015 #14
    If you're learning out of a book like Griffiths (about as basic as it'll get), all you really need is linear algebra, differential equations, and intro physics. Having seen Lagrangian/Hamiltonian Mechanics would help but isn't a requirement.

    Just because you see lots of formulas in a book doesn't mean that it's highly complex or mathematical; Griffiths likes to shotgun the reader with equations but they tend to be fairly straight forward. Also, having seen Classical prior to quantum is a good thing but is not a hard and fast requirement, especially when using Griffiths.
     
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