Prerequisites for Quantum Mechanics
Post Reply
 
Thread Rating:
  • 0 Votes - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
15-10-2016, 11:21 AM
Prerequisites for Quantum Mechanics
Hello physicists!

Quantum mechanics, really bugs the hell out of me. Specifically, me not being able to understand/accept it conceptually. So I want to learn about it more concretely and actually understand how things like wave functions and superposition are derived and used rather than somebody just telling me abstract things about them. But what prerequisites in physics and mathematics do I need to be able to study it?

For some background, I've taken AP Physics A which contains, I believe, classical mechanics/kinematics, including the mechanics of waves and sounds (no optics unfortunately), and a VERY basic introduction to electrostatics, including circuits. I also took AP Physics C (physics with calculus), but I only got through mechanics before I dropped the course (for personal reasons. No, I'm serious!). No experience with relativity. For math, I've completed multivariable calculus, though I could use a refresher.

Thanks!
Find all posts by this user
Like Post Quote this message in a reply
15-10-2016, 11:43 AM
RE: Prerequisites for Quantum Mechanics
(15-10-2016 11:21 AM)unknowndevil666 Wrote:  Hello physicists!

Quantum mechanics, really bugs the hell out of me. Specifically, me not being able to understand/accept it conceptually. So I want to learn about it more concretely and actually understand how things like wave functions and superposition are derived and used rather than somebody just telling me abstract things about them. But what prerequisites in physics and mathematics do I need to be able to study it?

For some background, I've taken AP Physics A which contains, I believe, classical mechanics/kinematics, including the mechanics of waves and sounds (no optics unfortunately), and a VERY basic introduction to electrostatics, including circuits. I also took AP Physics C (physics with calculus), but I only got through mechanics before I dropped the course (for personal reasons. No, I'm serious!). No experience with relativity. For math, I've completed multivariable calculus, though I could use a refresher.

Thanks!

Best bet is

Physics:

Calculus based Mechanics (Newtonian, Langrangian and Hamiltonian mechanics). Take the Sophomore and Junior level courses.

"Heat, Light and Sound" as a Sophomore level class if a Physics major- Optics and Waves (learn about Young's double slit experiment and diffraction/refraction of light waves).

Vector calculus-based Electromagnetism (and how Maxwell's equations lead to light and optics, definitly see the concept of a plane wave and wave equations in it) Take the Sophomore and Junior level courses.

On the math level:

Calculus (Basic integrals and differentiation should be second nature to you)

Linear Algebra (Most of Nonrelativistic Quantum Physics is one big eigenvalue problem)

Differential Equations and PDE's: You'll be mostly solving PDE's in Quantum Physics. So learn some basic techniques for it.

Probability Theory: to interpret results in a physical way you need to know about statistics and probability distributions. Take a Junior level class that uses Calculus, not the introductory freshman class.

Some of this you obviously have already covered. I wouldn't worry too much about retaking a class if you got a decent grade the first time. It'll come back to you. HTH

nb- I earned a B Sc in Physics in 1984, but most of it is dim history, as I didn't do any quantum mechanics at work.
Find all posts by this user
Like Post Quote this message in a reply
[+] 1 user Likes Fireball's post
15-10-2016, 01:14 PM
RE: Prerequisites for Quantum Mechanics
(15-10-2016 11:43 AM)Fireball Wrote:  Physics:

Vector calculus-based Electromagnetism (and how Maxwell's equations lead to light and optics, definitly see the concept of a plane wave and wave equations in it) Take the Sophomore and Junior level courses.


On the math level:

Linear Algebra (Most of Nonrelativistic Quantum Physics is one big eigenvalue problem)

Differential Equations and PDE's: You'll be mostly solving PDE's in Quantum Physics. So learn some basic techniques for it.

Thanks! Had I finished AP C I would've had all the physics done Facepalm. But that's more math than I was expecting (or hoping)...
Find all posts by this user
Like Post Quote this message in a reply
15-10-2016, 01:35 PM (This post was last modified: 15-10-2016 01:43 PM by cactus.)
RE: Prerequisites for Quantum Mechanics
Start here:













You'll want to learn about the Planck-Einstein relation, "E=hf", and then the Schrodinger Equation and how it's derived:
It's kind of advanced, though. Maybe Cal 3 level, since it involves partial derivatives



If we came from dust, then why is there still dust?
Find all posts by this user
Like Post Quote this message in a reply
[+] 1 user Likes cactus's post
15-10-2016, 02:39 PM
RE: Prerequisites for Quantum Mechanics
(15-10-2016 01:35 PM)cactus Wrote:  You'll want to learn about the Planck-Einstein relation, "E=hf", and then the Schrodinger Equation and how it's derived
...
It's kind of advanced, though. Maybe Cal 3 level, since it involves partial derivatives

Thumbsup That was extremely helpful
Find all posts by this user
Like Post Quote this message in a reply
16-10-2016, 04:55 AM
RE: Prerequisites for Quantum Mechanics
You'll need a firm grasp of university calculus III & university physics III.

I was taking calc III and tried a QM class.
I was the only student in the class and dropped it after a week.

Take as much calculus & physics as you can first.
I would also suggest geometry from an elementary perspective if your university has a class similar to that.

My first assignment in QM was to write a mathematical proof showing that 3 dimensions exist.

Insanity - doing the same thing over and over again and expecting different results
Find all posts by this user
Like Post Quote this message in a reply
16-10-2016, 05:53 AM
RE: Prerequisites for Quantum Mechanics
(16-10-2016 04:55 AM)Rahn127 Wrote:  You'll need a firm grasp of university calculus III & university physics III.

Does "university calculus" imply rigorous, proof-based mathematics? Like fundamental logic, set theory, that type of stuff.

Quote:My first assignment in QM was to write a mathematical proof showing that 3 dimensions exist.

Sounds fun!
Find all posts by this user
Like Post Quote this message in a reply
16-10-2016, 08:40 AM
RE: Prerequisites for Quantum Mechanics
(16-10-2016 05:53 AM)unknowndevil666 Wrote:  
(16-10-2016 04:55 AM)Rahn127 Wrote:  You'll need a firm grasp of university calculus III & university physics III.

Does "university calculus" imply rigorous, proof-based mathematics? Like fundamental logic, set theory, that type of stuff.

Quote:My first assignment in QM was to write a mathematical proof showing that 3 dimensions exist.

Sounds fun!

You're going to make me get out my calc book aren't you. I'll have to get back to you on that.

Insanity - doing the same thing over and over again and expecting different results
Find all posts by this user
Like Post Quote this message in a reply
16-10-2016, 09:21 AM
RE: Prerequisites for Quantum Mechanics
DiffeQ was so helpful to me.

"If we are honest—and scientists have to be—we must admit that religion is a jumble of false assertions, with no basis in reality.
The very idea of God is a product of the human imagination."
- Paul Dirac
Find all posts by this user
Like Post Quote this message in a reply
16-10-2016, 08:24 PM
RE: Prerequisites for Quantum Mechanics
My calc book wasn't as helpful as I had hoped, but here is a link to some notes on Calc III

http://tutorial.math.lamar.edu/Classes/C...lcIII.aspx

Insanity - doing the same thing over and over again and expecting different results
Find all posts by this user
Like Post Quote this message in a reply
Post Reply
Forum Jump: