Mathematical tools for quantum mechanics

In summary, the book is good but has a lot of mathematical content which may be too difficult for those without prior experience in the subject. There are alternatives available for those who are not confident in their mathematical skills.
  • #1
sodaboy7
81
0
I am currently reading the book on quantum mechanics by N.Zettili. It's really a good book but has a lot of mathematical stuff which I am not able to absorb. There's a whole chapter on mathematical tools but it is difficult to.understand. Can anyone suggest me book or text on mathematics as prerequisite for quantum mechanics?
 
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  • #2
Hey sodaboy7.

It would help the readers if you outlined your prior mathematical experience and any courses that you have taken, especially if they are calculus and linear algebra courses.
 
  • #3
chiro said:
Hey sodaboy7.

It would help the readers if you outlined your prior mathematical experience and any courses that you have taken, especially if they are calculus and linear algebra courses.

Sure. I have a firm grip on high school mathematics and 2 semesters of engineering mathematics (and 3 sem is going on). It will be better if book/text is meant for I year or II year Undergraduates.
 
  • #4
Have you done multivariable calculus, differential equations, and linear algebra?
 
  • #5
Yes. Done with it.
 
  • #6
sodaboy7 said:
Yes. Done with it.

I read Zettili with same preparation. I had no problem understanding it.
 
  • #7
YAHA said:
I read Zettili with same preparation. I had no problem understanding it.

Maybe my coursework is elementary.
 
  • #8
sodaboy7 said:
Maybe my coursework is elementary.

From personal experience, I found that most concepts from Linear Algebra and some analysis (orthogonality of functions) need to be coldly understood. That math chapter in Zettili is important as he uses the techniques from it in later chapters without many (or with very brief) elaborations.

However, if you can get through it, you will come out stronger on the other side. He probably has the best explanation of the bra-ket notation out there.
 
  • #9
Perhaps, it is the Physics that you don't understand? You can't just jump right into QM without a background in Physics.
 
  • #10
Try Shankars book - I found it a lot easier to learn from than Zettilli..
As for preperation; linear algebra. Linear algebra is where the real meat of the subject is, the calculus, mindless churning out solutions to PDEs, part of it isn't where the understanding lies.5
Gilbert Strang - Introduction to Linear Algebra
Hoffman - Linear Algebra
Steve Roman - Advanced Linear Algebra
Pick one of those depending on your current skill level (although if you're already at hoffman level the new material in romans book won't really add much).
 
  • #11
To give reference to my level I would say I am almost done with calculus by Thomas and Finney.
 
  • #12
Ivan92 said:
Perhaps, it is the Physics that you don't understand? You can't just jump right into QM without a background in Physics.

No. I don't have any problem there. But I have not studied relativity yet. So should I go for relativity before QM?
 
  • #13
sodaboy7 said:
No. I don't have any problem there. But I have not studied relativity yet. So should I go for relativity before QM?
QM is essentially a non-relativistic theory so SR is not an necessary pre-req.

In terms of Zetilli's Chapter 2, I agree that there's quite a bit of material in there and if you haven't taken a serious course in linear algebra covering a good deal of material on self-adjoint operators, you might find the material too condensed as he only states theorems without proving it and thus there's a lot of facts packed in one page.
 

1. What are some of the basic mathematical concepts used in quantum mechanics?

Some of the basic mathematical concepts used in quantum mechanics include linear algebra, complex numbers, probability theory, and differential equations.

2. How is matrix algebra used in quantum mechanics?

Matrix algebra is used in quantum mechanics to represent physical systems and their states. It allows for the manipulation and calculation of quantum states and observables.

3. What is the role of operators in quantum mechanics?

Operators are used in quantum mechanics to represent physical quantities, such as position, momentum, and energy. They act on quantum states to produce new states and can be used to calculate the probabilities of different measurement outcomes.

4. How is probability theory applied in quantum mechanics?

Probability theory is used in quantum mechanics to calculate the probabilities of different measurement outcomes. The wave function, which represents the state of a quantum system, gives the probability of finding the system in a particular state.

5. What are some common mathematical tools used in solving quantum mechanics problems?

Some common mathematical tools used in solving quantum mechanics problems include the Schrödinger equation, the Heisenberg uncertainty principle, and the Born rule. Other tools such as Fourier transforms, eigenvalue problems, and tensor products are also frequently used.

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