Mathematical Requirements for Basic Quantum Physics

In summary, to be able to follow the formulas and principles in a quite basic quantum mechanics book, you only need partial differential equations, statistics and probability, linear algebra, and Hilbert spaces. Partial differential equations, statistics and probability, linear algebra, and Hilbert spaces are all standard undergraduate level mathematics courses. If you want to be able to understand the more complex concepts in a quantum mechanics book, you may need to take more advanced math courses.
  • #1
Nano-Passion
1,291
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I want to be able to follow basic books for quantum physics to get a taste of some of the underlying principles. The problem is: I don't even know half of the symbols.

So basically, what mathematical knowledge is needed to be able to follow the formulas and principles in a quite basic quantum mechanics book?
 
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  • #2
Partial Differential Equations
Statistics and Probability
Linear Algebra
Hilbert spaces
 
  • #3
Functor97 said:
Partial Differential Equations
Statistics and Probability
Linear Algebra
Hilbert spaces

Do I only need to touch over certain concepts of these subjects or is a deeper understanding needed and I have to wait to take all the classes?
 
  • #4
Nano-Passion said:
So basically, what mathematical knowledge is needed to be able to follow the formulas and principles in a quite basic quantum mechanics book?

Functor97 said:
Partial Differential Equations
Statistics and Probability
Linear Algebra
Hilbert spaces

Do you really think that knowledge all of these things is necessary before studying "a quite basic quantum mechanics book?"
 
  • #5
George Jones said:
Do you really think that knowledge all of these things is necessary before studying "a quite basic quantum mechanics book?"

Sorry George, i did not read the "simple" qualifier. How simple are we talking? Why not get a Brian Greene or Stephan Hawking book, there are no equations in those, but that does limit understanding. It would help if you posted the titles of the books you are having trouble understanding.
 
  • #6
Nano-Passion said:
Do I only need to touch over certain concepts of these subjects or is a deeper understanding needed and I have to wait to take all the classes?

It depends how well you want to understand QM?
 
  • #7
Functor97 said:
Sorry George, i did not read the "simple" qualifier. How simple are we talking? Why not get a Brian Greene or Stephan Hawking book, there are no equations in those, but that does limit understanding. It would help if you posted the titles of the books you are having trouble understanding.

First: Welcome to Physics Forums!

Note that I am not the original poster and I didn't write anything about trouble with understanding quantum mechanics books. I think we have a difference of opinion, but that doesn't mean that we can't discuss this difference of opinion calmly. :smile:

How simple? Any standard final-year undergrad quantum mechanics text.
 
  • #8
George Jones said:
First: Welcome to Physics Forums!

Note that I am not the original poster and I didn't write anything about trouble with understanding quantum mechanics books. I think we have a difference of opinion, but that doesn't mean that we can't discuss this difference of opinion calmly. :smile:

How simple? Any standard final-year undergrad quantum mechanics text.

Sorry, i was referring to the op after the first line. I did not mean to say you had trouble understanding.

If it is a final year undergrad physics book, i believe linear algebra, differential equations and probability would suffice.
 
  • #9
Functor97 said:
If it is a final year undergrad physics book, i believe linear algebra, differential equations and probability would suffice.

If Nano-Passion meant something easier than this, something like

https://www.amazon.com/dp/047187373X/?tag=pfamazon01-20

or a text for a North American Modern Physics course, then I would say multivariable calculus and maybe basic intros to the stuff that you have listed.

I am not trying to discourage the study of mathematics, I like mathematics, but not much is needed to study introductory, quantitative physics texts.
George Jones said:
As a physics major, I took many math courses that weren't required (for example, analysis, abstract algebra, functional analysis, topology, measure theory, etc.), and, as a physics grad student, I took three grad pure mathematics courses in representation theory and differential geometry.
 
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  • #10
George Jones said:
If Nano-Passion meant something easier than this, something like

https://www.amazon.com/dp/047187373X/?tag=pfamazon01-20

or a text for a North American Modern Physics course, then I would say multivariable calculus and maybe basic intros to the stuff that you have listed.

I am not trying to discourage the study of mathematics, I like mathematics, but not much is needed to study introductory, quantitative physics texts.

Yes, this is exactly the kind of book that I was talking about! I want to dive into some non-intuitive stuff instead of classical mechanics. Though I fell in love with the power and mathematical prediction that classical mechanics came with its starting to become bland to me now. I took physics in high school, later I had to take physical science which was basically a recap, and now I have to go over calculus-based mechanics again!

I would have to wait an awefully long while so I want to run through some of the basic quantum mechanic principles because I find them so bewildering.

Anyways enough of my rambling, I'm pretty lost on where to begin in self-studying the required mathematics. Is multivariable calculus basically a different name for calculus III? If not then what is it?

I'm just self-teaching myself calculus at the moment till my fall semester starts so it sounds like I have a long while to go unless I know exactly what mathematical concepts I need. Please help. ^.^
 
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  • #11
Nano-Passion said:
Is multivariable calculus basically a different name for calculus III?

Yes.
Nano-Passion said:
I'm just self-teaching myself calculus at the moment till my fall semester starts so it sounds like I have a long while to go unless I know exactly what mathematical concepts I need. Please help. ^.^

Prerequisites for the book probably are Calc I, II, III.
 
  • #12
For intro modern physics books that also present an introduction to the mathematics of QM, but are "easier" than Eisberg & Resnick (which IMO is pretty tough slogging for many students, with lots of text), consider:

https://www.amazon.com/dp/013805715X/?tag=pfamazon01-20

https://www.amazon.com/dp/B004K3BK5W/?tag=pfamazon01-20

https://www.amazon.com/dp/0131244396/?tag=pfamazon01-20

I used Taylor et al. when I taught this course most recently. All you absolutely need is a fair working knowledge of single-variable calculus (derivatives and integrals), and an acquaintance with partial derivatives from multivariable calculus. As I recall (I don't have the book handy to check), it introduces/reviews complex variables and basic probability as needed, and the basic concept of a differential equation. It presents the basic stuff about the wave function, normalization, expectation values, the "particle in a box" and other simple one-dimensional examples. It outlines the solution of the Schrödinger Equation for the hydrogen atom without filling in all the gory details (for example, it derives the differential equation for the theta-part of the solution, and then basically says "the solutions are called spherical harmonics, and here's a table of some of them"), focusing on the quantum numbers and their significance.

After doing something like this, you're better prepared for a full-blown QM course using a textbook like Griffiths or Morrison, etc.
 
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  • #13
Nano-Passion said:
I want to be able to follow basic books for quantum physics to get a taste of some of the underlying principles. The problem is: I don't even know half of the symbols.

So basically, what mathematical knowledge is needed to be able to follow the formulas and principles in a quite basic quantum mechanics book?

In my Chem I class we learned about QM for 3 chapters. It doesn't have much math but I learned the big ideas. I know you said you want to learn the physics but a conceptual understanding can never hurt. Good luck.
 
  • #14
As of now I am up to the chain rule. I think I might skip around and teach myself the basics needed because I want to dive into some of the stuff in quantum physics already.

Things that I will teach myself is integration, basics of differential equations, polar coordinates, "vectors and the geometry of space", "vector-valued functions", multiple integration?, and some "vector analysis".

Whats in quotes is simply the chapter title. I would study these and whatever material needed in between I will refer back to and learn it. I was given that idea by someone else and I liked it.

Thoughts? I don't really know much at all of what is really needed but just have a little idea looking through my calculus textbook.
 
  • #15
jtbell said:
For intro modern physics books that also present an introduction to the mathematics of QM, but are "easier" than Eisberg & Resnick (which IMO is pretty tough slogging for many students, with lots of text), consider:

https://www.amazon.com/dp/013805715X/?tag=pfamazon01-20

https://www.amazon.com/dp/B004K3BK5W/?tag=pfamazon01-20

https://www.amazon.com/dp/0131244396/?tag=pfamazon01-20

I used Taylor et al. when I taught this course most recently. All you absolutely need is a fair working knowledge of single-variable calculus (derivatives and integrals), and an acquaintance with partial derivatives from multivariable calculus. As I recall (I don't have the book handy to check), it introduces/reviews complex variables and basic probability as needed, and the basic concept of a differential equation. It presents the basic stuff about the wave function, normalization, expectation values, the "particle in a box" and other simple one-dimensional examples. It outlines the solution of the Schrödinger Equation for the hydrogen atom without filling in all the gory details (for example, it derives the differential equation for the theta-part of the solution, and then basically says "the solutions are called spherical harmonics, and here's a table of some of them"), focusing on the quantum numbers and their significance.

After doing something like this, you're better prepared for a full-blown QM course using a textbook like Griffiths or Morrison, etc.

Wow, the book by Ohanian is available for only 12 dollars including shipping? 0__o

It sounds good, but I was thinking about following an introductory to mechanics book from college. Such as Principles of Quantum Mechanics by Shankar :

https://www.amazon.com/dp/0306447908/?tag=pfamazon01-20

or Quantum Mechanics: an Introduction by Greiner

https://www.amazon.com/dp/3540780459/?tag=pfamazon01-20


Its style caught my attention. What would be better to follow one of these books (with no cost might I add =p) or a textbook by Ohanian?
 
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Related to Mathematical Requirements for Basic Quantum Physics

1. What is the mathematical foundation of basic quantum physics?

The mathematical foundation of basic quantum physics is based on linear algebra, complex numbers, and functional analysis. These mathematical tools are used to represent and manipulate quantum states and operators.

2. How important is mathematical rigor in understanding quantum physics?

Mathematical rigor is extremely important in understanding quantum physics. Without a solid mathematical foundation, it can be difficult to fully grasp the concepts and principles of quantum mechanics.

3. What are some common mathematical concepts used in basic quantum physics?

Some common mathematical concepts used in basic quantum physics include Hilbert spaces, matrix algebra, eigenvalues and eigenvectors, and probability theory. These concepts are essential in representing and understanding quantum systems.

4. Can one study quantum physics without a strong background in mathematics?

While a strong background in mathematics is highly recommended for studying quantum physics, it is possible to learn the basics without extensive mathematical knowledge. However, a deeper understanding and appreciation of the subject will require a solid understanding of mathematical concepts.

5. How does the mathematical framework of quantum physics differ from classical physics?

The mathematical framework of quantum physics differs from classical physics in several ways. One key difference is the use of complex numbers and linear algebra to represent quantum states, as opposed to real numbers and vector calculus in classical physics. Additionally, the concept of superposition and the measurement problem are unique to quantum mechanics and require a different mathematical approach compared to classical mechanics.

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