Sources to learn about Berry phases and Adiabatic Theorem

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SUMMARY

The discussion centers on resources for understanding Berry phases and the Adiabatic Theorem in quantum mechanics. Participants recommend Griffiths' "Quantum Mechanics" for foundational knowledge, specifically highlighting the chapters on the Adiabatic Theorem and the Aharonov-Bohm effect. Additionally, Sakurai's "Modern Quantum Mechanics" is suggested, particularly chapters 2 and 5, as a valuable resource for deeper insights into these topics. The consensus is that a solid grasp of the initial chapters of Griffiths and Shankar will prepare undergraduate students to tackle Sakurai's material effectively.

PREREQUISITES
  • Familiarity with Griffiths' "Quantum Mechanics" (at least the first half)
  • Understanding of Shankar's "Principles of Quantum Mechanics"
  • Basic concepts of Berry phases and the Adiabatic Theorem
  • Knowledge of the Aharonov-Bohm effect
NEXT STEPS
  • Read Griffiths' "Quantum Mechanics" chapters on the Adiabatic Theorem and Aharonov-Bohm effect
  • Study Sakurai's "Modern Quantum Mechanics" chapters 2 and 5 for advanced insights
  • Explore additional resources on Berry phases in quantum mechanics
  • Investigate the mathematical foundations of the Adiabatic Theorem
USEFUL FOR

Undergraduate students in physics, particularly those studying quantum mechanics, as well as educators seeking to enhance their understanding of Berry phases and the Adiabatic Theorem.

Joker93
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Hello,
I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect.
As I found them very interesting, I would appreciate if anyone could provide me with some good sources(books, internet links etc) to learn more about them.
Please keep in mind that I am only an undergraduate student, so difficult graduate stuff might not be of very use for me.
Thanks in advance!
 
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Sakurai explains it quite well in chapter 5. Chapter 2 includes the aharonov boom effect which is then covered again in chapter 5.
 
radium said:
Sakurai explains it quite well in chapter 5. Chapter 2 includes the aharonov boom effect which is then covered again in chapter 5.
thanks for answering!But isn't sakurai a graduates test?
 
After you've read the first half of Griffiths you should be able to understand it. When I learned quantum mechanics, I read the first few chapters of Griffiths and Shankar and then went straight to Sakurai. Also, the adiabatic theorem and Berry's phases are very subtle topics. In order to understand them well you need to know a lot of the stuff in Sakurai at least.
 
radium said:
After you've read the first half of Griffiths you should be able to understand it. When I learned quantum mechanics, I read the first few chapters of Griffiths and Shankar and then went straight to Sakurai. Also, the adiabatic theorem and Berry's phases are very subtle topics. In order to understand them well you need to know a lot of the stuff in Sakurai at least.
ok,thanks..
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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