Mathematical tools for quantum mechanics

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Discussion Overview

The discussion revolves around the mathematical prerequisites for understanding quantum mechanics, specifically in relation to the book by N. Zettili. Participants share their experiences with mathematical tools and suggest resources for those struggling with the mathematical aspects of quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant expresses difficulty in absorbing the mathematical content of Zettili's book and seeks recommendations for prerequisite texts.
  • Several participants suggest outlining prior mathematical experience to better tailor recommendations.
  • One participant mentions having a solid foundation in high school mathematics and engineering mathematics, indicating a preference for undergraduate-level texts.
  • Another participant confirms completion of multivariable calculus, differential equations, and linear algebra, stating they had no issues with Zettili's book.
  • Some participants emphasize the importance of understanding linear algebra and certain analysis concepts, such as orthogonality of functions, for grasping quantum mechanics.
  • One participant suggests that a lack of understanding may stem from insufficient physics background rather than mathematics.
  • Recommendations for alternative texts include Shankar's book and various linear algebra resources, with comments on their accessibility compared to Zettili's work.
  • There is a discussion about the necessity of studying relativity before quantum mechanics, with one participant asserting that quantum mechanics is fundamentally a non-relativistic theory.
  • Concerns are raised about the condensed presentation of material in Zettili's Chapter 2, particularly regarding self-adjoint operators and the lack of proofs for stated theorems.

Areas of Agreement / Disagreement

Participants express differing opinions on the adequacy of their mathematical backgrounds for understanding quantum mechanics, with some feeling confident and others suggesting additional preparation may be necessary. There is no consensus on whether relativity should be studied prior to quantum mechanics, as opinions vary on its relevance.

Contextual Notes

Some participants note that the mathematical chapter in Zettili is crucial for later understanding, but its presentation may be challenging without a solid foundation in linear algebra and related concepts. The discussion reflects varying levels of preparedness and the subjective nature of learning quantum mechanics.

sodaboy7
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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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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.
 
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.
 
Have you done multivariable calculus, differential equations, and linear algebra?
 
Yes. Done with it.
 
sodaboy7 said:
Yes. Done with it.

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

Maybe my coursework is elementary.
 
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.
 
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.
 

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