Is Quantum Mechanics hard to understand/learn? and if so... why?

Question

I want to learn QM. Do you have any advice or warnings? websites? books?

thanks.

Answer 1

Quantum Mechanics is hard in two ways:

(1) mathematical formalism - it requires a deeper level of mastery of mathematics, and also QM is a theory of probabilities.

(2) interpretation of physical reality - so what does the result of probability function tell us? this is not easy to figure out.

So when the previous answerer say that even Richard Feyman tells us that no one understand quantum physics, this is what he means - that no one can understand the physical reality that QM presents to us, not that he can't understand the math. Richard Feyman actually invented a whole mathematical approach to solving QM problems, so that definitely was not his problem.

Answer 2

It's 'hard' to learn because it requires a solid mathematical background (calc I and II, linear algebra, and differential equations at the least) to approach, and it's very non-intuitive.

The most basic textbook for QM is Griffith's Introduction to Quantum Mechanics. This book is typically used for third or fourth year undergraduate physics majors. If you don't have that kind of a math and physics background, you might want to start with the basics.

Answer 3

Hi,

QM is indeed difficult to learn. One reason is that it can involve some pretty sophisticated math. To really tackle it, I suggest brushing up on vector calculus and linear algebra.

If you only want to understand it conceptually, and not in details, then you can skip some of the math. In this case, the tough part of QM is that it is very counter-intuitive at times. In many simple physics problems, you can tell if your answers are absurd as soon as you see them: if you do a projectile motion problem and find a bullet traveling faster than the speed of light, for instance, you know you messed up. But in QM, the correct predictions/solutions are often the least intuitive ones. If you are the type who really needs to visualize and intuit your way, QM can be very tough. This is one of the reasons why math is so important - the typical reality checks we perform on our answers aren't very useful in QM!

Hope this helps. You may consider looking at a QM textbook by Griffiths, if you want a good start. It can be mathematical, but it's not overwhelming.

Answer 4

quantum mechanics proves to be quite hard to most but this does not mean you cannot excel. you can excel in something that is hard. you are on the right track. let me direct you to this link. http://grenouille-bouillie.blogspot.com/2007/10/quantum-mechanics-for-dummies.html
this info in this link would have helped me greatly. back when i took the class it was no such thing as no internet. back then, the only people you could aks for help was people who was competing for the same grade you was competing for. now with the internet, you could reach out to people who you dont present any threat to and get good help. i just read the article in the link for less than 30 seconds and got basic questions answered that i never got answered during a whole semester at school surrounded by people who was scared i might get a better grade than they got. may i present you with some of them now? they may help you. quantum mech: 1)what are we doing and 2)why are we doing it and 3) how do we do it.
from the article i found out that we are trying to find out mathematically where an electron is at. an electron like the one in the hydrogen atom goes all around the nucleus. quantum mechanics wants to derive a mathematical equation that tells you were it is. now go to the article in the link and note the word "presence". we want to know where this thing is. 2) i dont know why but i have a good guess....just pure science. scientist always want to know why. 3) how? with a combination of mathematical 'wave' equations and statistical equations becaue an electron moves in ways similar to how light moves and wave equations will mathematically tell its position. also the equation does not try to pinpoint the location of the electron but instead it gives a sort of probability percentage and says "the electoron will be between coordinates x1,y and x2,y 40% of the time". please read this article also. http://en.wikipedia.org/wiki/Particle_in_a_box.
how do we do it? we build a model that acts like and represents an electron trapped in orbit around a nucleus. a particle in a box acts JUST LIKE a electron orbiting a hydrogen nucleus. when we solve the particle in a box we have a set of equations that tell us where an electron is likely to be. does this help?

Answer 5

If you have a good understanding of mathematics (including linear vector spaces, calculus, complex numbers, Fourier transforms) and classical physics (Lagrangian & Hamiltonian mechanics, electromagnetism, relativity), you can learn quantum mechanics. Understanding it is another story altogether. My advice to you is to give up trying to understand how it even works, just do the math. Even Richard Feymann, one of the most brilliant quantum physicists ever, had this to say about the subject, "I can safely say that nobody understands quantum physics!"

Addendum: Thanks, PhysicsDude, for your comments about Feymann.

Answer 6

Your question is a difficult one to answer -- some people find quantum mechanics harder to learn than others. I personally found it to be a lot easier to learn than electicity and magnetism (the intermediate-level class that requires vector calculus, not the freshman class) or thermodynamics, or even electronics. As for understanding quantum mechanics, it's not too bad to understand, as long as you alter your notion of what "understanding" is. Don't assume that you can use your physical intuition in every problem, because everyone's physical intuition is initially based off of what they observe in the world around them, which behaves in a classical (not quantum mechanical) way. Your intuition in quantum mechanics has to be more linked to the mathematical formalism -- but that isn't to say that you can't develop a quite strong quantum mechanical intuition indeed!

Studying quantum mechanics does require some math skills, but don't let that daunt you. When I started studying quantum mechanics I only had taken math classes through calculus. If you're teaching yourself quantum mechanics, you can teach yourself a lot of the necessary math too (although bear in mind that you might not be as good at the math as you would be if you took an actual class in it). (Anecdote: Once when I was visiting graduate schools I talked with a professor of theoretical chemistry at Caltech, and he asked what kind of math background I had. I said I had taken calculus in high school and a semester of differential equations in college and had taught myself the rest during my chemistry and physics classes. He said, "Good, you probably learned it right, then.") It would probably help if you've had a calculus class before you start learning quantum mechanics, just to know what integrals and derivatives are and how to do basic ones (or know how to look them up in tables). You'll need to know what complex numbers are and how to work with them (how to take complex conjugates, how to use the Euler equation/polar representation of complex numbers), the basic trigonometric functions (sine, cosine, etc.), exponential functions, etc. You'll need to know how to work with vectors and take dot products. You'll need to know how to do basic integrals (for example, involving exponentials and trigonometric functions) and how to work in different coordinate systems (Cartesian coordinates, spherical polar coordinates, etc.). You'll need to know basic probability theory (e.g., how to take an average of a random variable given a probability density function). It's also good to know some matrix algebra (how to multiply matrices and vectors, take transposes, use matrix notation, etc.). You'll already know most of these things if you've taken high school/college math through calculus and done well. These are the things that are good to know before you start learning quantum mechanics. It sounds like a lot, but most of these things aren't too difficult, they just need some formal study. Just have your trusty calculus book by your side when you study quantum mechanics.

Also, you should have some basic physics knowledge before beginning -- high school/first year of college knowledge about forces, energy, electricity and magnetism, and waves, and enough chemistry/physics to know about atomic orbitals and things like that.

Here are some things that you'll need to learn while learning quantum mechanics, if you don't already know them. The most basic equation in quantum mechanics is the Schrodinger Equation, which is a differential equation. You can understand and solve the most basic differential equations just by substituting a trial solution into the equation, particularly if your solutions are just exponential or trigonometric functions. But if you want to solve any serious quantum-mechanical problem (the harmonic oscillator, the hydrogen atom, etc.), you'll need to know the tricks they use in differential equations classes. I think most quantum mechanics textbooks that actually solve these problems show you the relevant tricks, but it wouldn't hurt if you had a differential equations book by your side to help you out. Also, the linear algebra gets more serious, because you spend a lot of time solving eigenvalue equations, which requires you to be able to solve matrix determinants to find eigenvalues and eigenvectors. Again, a good book will show that process explicitly, but it doesn't hurt to have a linear algebra book by your side when you learn that.

I've taken at least a dozen classes in quantum mechanics, and I have dozens of books (each one of which is my favorite for a different topic in quantum mechanics), and the strongest recommendation I can make for a new student of quantum mechanics is to start out learning Dirac notation from the beginning. Almost no college classes do this, I think because they have to cover a lot of material in a limited amount of time, so they want to start out with math that is already familiar to the student, like calculus. But if you're studying on your own, start learning quantum mechanics at the same time as you learn Dirac notation (the bracket or "bra-ket" formalism). Spend a couple of months getting intimate with that notation. It's not that heard to learn, and it will give you a HUGE advantage over everyone else. The problem with Dirac notation is that it's based more in the linear algebra formalism of quantum mechanics than in the calculus formalism (although the notation allows you to easily translate between the two), so it takes a little while to figure out what you're doing and what it means. As another poster said, don't worry at first about your physical intuition, just do the math. I think you'll find that if you ever develop a physical intuition into quantum mechanics at all, that intuition will be in the language of the Dirac notation. The best recommendation I can make is to get the book "Primer of Quantum Mechanics" by Marvin Chester and get as far as you can through it (including working the problems). That's the book from which I first learned quantum mechanics for real the summer after my first year in college. Also, the Feynman Lectures on Physics (Volume III) is good, especially the discussion of the two-slit interference problem. Once you get more advanced, you can look at the books by Sakurai (Modern Quantum Mechanics) and Shankar (Principles of Quantum Mechanics, 2nd edition), which are very math-based but also use the Dirac notation in a straightforward way. This notation is really the "natural language" of quantum mechanics (in my opinion), and it will make solving many problems so much easier. Sometimes you'll have to translate into another "language" (like calculus), but that's very straightforward. Once you go Dirac, you can't go back. You'll be much better prepared for any serious study of quantum mechanics, using any more standard textbook or while taking any more traditional class.

My advice is not to go too far in a purely qualitative (conceptual) study of quantum mechanics, and not to get too upset by the question, "Why does the particle act that way?" These are the mistakes that drive the majority of people out of quantum mechanics, and I think that lead to the majority of misunderstandings about quantum mechanics. What you need to know about quantum mechanics is that things on the microscopic level behave very differently from what we know from our everyday experience. Don't ask "why?" too much, that's just how nature works. People always want to frame quantum mechanics in terms of their classical understanding of things, but that's misguided. The only reason we have a classical understanding of things to begin with is because we can't directly perceive the quantum world, we have to access it indirectly through experiments. In reality, the classical, everyday world obeys the laws of quantum mechanics too, but in the macroscopic world the uniquely quantum effects are so small that we generally can't perceive or even measure them anymore.

Don't run down the rabbit hole of all the weird schools of thought on the interpretation of quantum mechanics, either (measurement, consciousness, the "paradoxes," etc.). Those are deep, fundamental problems, but most people get lost in that world because they first haven't learned common, everyday quantum mechanics, which includes a lot of solving problems using mathematics. The best (in my opinion, the only) way to learn quantum mechanics is to solve a lot of problems, to examine many quantum systems and try to learn everything about them that can be calculated or measured. Don't worry too much about what the particle is "doing" when no one is "looking" at it. It's a tree-falls-in-the-forest type question. Some questions are ill-posed, so they just don't have clear answers. Focus on what you can observe and measure. That's all you can possibly know about a quantum system, take it from Heisenberg! Calculate, calculate, calculate.

Above all, have fun. As you start to learn, try to identify what type of problems are the most fun for you, and just play with them. The only way anyone really learns anything well is by being interested in the problem, and having fun.

Good luck in your studies!