Rigoruos Pertubation Theory.

In summary, there are several recommended textbooks for rigorous treatments of mathematical physics, including Reed and Simon's Methods of Modern Mathematical Physics, Thirring's A Course in Mathematical Physics, and Ballentine's textbook on quantum mechanics. However, while these texts are thorough and mathematically rigorous, some proofs may still be missing and need to be supplied by the reader.
  • #1

MathematicalPhysicist

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Anyone has any recommendation for a textbook/s that doesn't shun away from proofs of theorems?

I read Murdock's text, but he says himself that he doesn't cover it all.
And Bender's methods is more on exercising the methods than understanding them.

Any?

Thanks.
 
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  • #2
MathematicalPhysicist said:
Anyone has any recommendation for a textbook/s that doesn't shun away from proofs of theorems?

Reed and Simon, Methods of Modern Mathematical Physics, Vol. I+II

Thirring, A course in mathematical physics, Vol. III
 
  • #3
And all the pertubation theory theorems (the main ones) are proven in Reed's and Simon's?

I really should be reading this series if I want to really be a mathematical physicist. :-)

Thanks.
 
  • #4
MathematicalPhysicist said:
And all the perturbation theory theorems (the main ones) are proven in Reed's and Simon's?

R&S is quite thorough, and mathematically rigorous. Moreover, each Chapter comes with long, detailed notes on references where proofs can be found for all the stuff they didn't prove. Only the newer things (post 1980?) are not included - but most of perturbation theory is very old.
 
  • #5
Have you tried Ballentine? Way more rigorous treatment of quantum mechanics than the books you see in undergrad.
 
  • #6
Klockan3 said:
Have you tried Ballentine? Way more rigorous treatment of quantum mechanics than the books you see in undergrad.

But very far from being a rigorous text with rigorous proofs.
 
  • #7
Mathematical Aspects of Classical and Celestial Mechanics by Arnold etc. (not to be confused with the textbook Mathematical Methods of Classical Mechanics by the same author) is clear, excellent, and encyclopedic. However, most of the proofs are missing and are to be supplied by the reader. Not necessarily a bad thing though.
 

1. What is Rigorous Perturbation Theory?

Rigorous Perturbation Theory is a mathematical method used to solve complex systems by breaking them down into simpler, solvable parts. It is commonly used in physics, engineering, and other scientific fields to find approximate solutions to problems that cannot be solved exactly.

2. How does Rigorous Perturbation Theory work?

Rigorous Perturbation Theory works by assuming that the solution to a complex problem can be expressed as a series of simpler solutions. Each subsequent solution in the series is an improvement upon the previous one, and the process continues until the desired level of accuracy is achieved.

3. What are the advantages of using Rigorous Perturbation Theory?

Rigorous Perturbation Theory allows scientists to solve complex problems that would otherwise be impossible to solve using traditional methods. It also provides a systematic approach to finding approximate solutions, making it easier to understand and analyze the results.

4. What are the limitations of Rigorous Perturbation Theory?

One limitation of Rigorous Perturbation Theory is that it can only be used for problems where there is a small parameter that can be used to simplify the problem. It also relies on the assumption that the solution can be expressed as a series, which may not always be accurate.

5. Can Rigorous Perturbation Theory be used in all scientific fields?

Rigorous Perturbation Theory is most commonly used in physics, but it can also be applied to other scientific fields such as chemistry, biology, and engineering. However, its applicability may vary depending on the complexity of the problem and the availability of a small parameter to simplify it.

Suggested for: Rigoruos Pertubation Theory.

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