Mathematical prerequisites for Quantum Mechanics

In summary, to completely understand Landau's and Lifschitz's textbook on Quantum Mechanics, it is recommended to have a strong understanding of algebra, linear algebra, calculus, and differential equations. Alternatively, studying books on vector analysis, ordinary and partial differential equations, functional analysis, and differential geometry can provide a better grounding for the long run. However, these may not be necessary for a basic understanding of the material. Additionally, there are no rigorous QM textbooks available, as it would require a significant amount of time to learn the necessary math. Instead, it is recommended to focus on studying linear algebra, with the book "Axler" being a suggested resource. Another suggested textbook is "Reed and Simon, Methods of Modern Mathematical Physics
  • #1
D.K.
12
0
So, I am about to read Landau's and Lifschitz's textbook on Quantum Mechanics. What kind of mathematics I should be already familiar with in order to completely understand the above mentioned material?

Thanks for all the advice.
 
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  • #2
Algebra, Linear Algebra, Calculus, and Differential Equations

If you want to power through it all, you can do so here in possibly the most efficient form.

http://tutorial.math.lamar.edu/
 
  • #3
D.K. said:
So, I am about to read Landau's and Lifschitz's textbook on Quantum Mechanics. What kind of mathematics I should be already familiar with in order to completely understand the above mentioned material?
Since you are already about to read it, just start, and note while reading the concepts you are not yet sufficiently familiar with. Then look these up and practice their use.
This recipe works for anything you read at anytime, and it gives you precisely the minimal amount that you need.

Alternatively, first read (and practice with) books about vector analysis, ordinary and partial differential equations, functional analysis, differential geometry, etc.. This will give you a much better grounding for the long run, but will be much more than what you need at first.
 
  • #4
Another thread on <mathematical prerequisites>. Well, all depends on how deep in knowing and understanding a particular physical theory you wish to get. L & L's book does indeed teach you a lot of physics and phenomenology at the price (but most books pay this price) of keeping mathematical rigor to a mininum.

So yes, linear algebra and calculus: real and complex + Fourier transformations should be handled decently before going to an involved reading of the book you mention.
 
  • #5
dextercioby said:
L & L's book does indeed teach you a lot of physics and phenomenology at the price (but most books pay this price) of keeping mathematical rigor to a mininum.

Well, that's quite surprising to hear. Would you be so kind as to recommend a quantum mechanic textbook that in your opinion is the best when it comes to math rigor?
 
  • #6
D.K. said:
Well, that's quite surprising to hear. Would you be so kind as to recommend a quantum mechanic textbook that in your opinion is the best when it comes to math rigor?
I don't think there are any rigorous QM books. The problem is that it would take a typical QM student at least a year, probably two, to learn all the math (in particular topology and functional analysis) they need to understand the mathematics of QM.

People always mention differential equations in these threads. (There are lots of them). I always feel compelled to say that there's only one differential equation in the theory, and the QM book will tell you how to solve it. So studying a book on differential equations won't help you at all to prepare for QM, other than by giving you some mathematical maturity. You're much better off studying linear algebra. I recommend Axler.
 
  • #7
D.K. said:
Would you be so kind as to recommend a quantum mechanic textbook that in your opinion is the best when it comes to math rigor?
Reed and Simon, Methods of Modern Mathematical Physics. 4 Vols.
(This includes all functional analysis needed.)
 

1. What mathematical concepts are necessary to understand Quantum Mechanics?

The main mathematical prerequisites for Quantum Mechanics include linear algebra, complex numbers, and calculus. It is also helpful to have knowledge of differential equations and probability theory.

2. How important is linear algebra in understanding Quantum Mechanics?

Linear algebra is essential in Quantum Mechanics as it is used to describe the state of quantum systems, such as particles and atoms. It helps in the understanding of quantum superposition, entanglement, and measurement.

3. What is the role of complex numbers in Quantum Mechanics?

Complex numbers are used to describe the wave-like behavior of quantum particles. They are also essential in representing the state of a quantum system and calculating probabilities of measurements.

4. Do I need advanced calculus knowledge to understand Quantum Mechanics?

Having a solid understanding of calculus is necessary for understanding the mathematical foundations of Quantum Mechanics. This includes knowledge of derivatives, integrals, and differential equations.

5. How does probability theory relate to Quantum Mechanics?

Probability theory is used extensively in Quantum Mechanics to predict the outcomes of measurements on quantum systems. It is also used to describe the probabilistic nature of quantum particles and their behavior.

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