Perturbation Theory: Calculating 1st-Order Correction

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SUMMARY

This discussion centers on the calculation of the first-order correction in Perturbation Theory (PT) within quantum mechanics. Participants reference key texts such as Sakurai, Gasiorowicz, Zettili, and Griffiths, highlighting that while first-order corrections are commonly covered, second-order corrections are also addressed in Griffiths' work. The conversation emphasizes the need for clear examples and methodologies for calculating these corrections, particularly for those struggling with higher-level texts.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with Perturbation Theory concepts
  • Knowledge of first-order and second-order corrections
  • Ability to interpret mathematical formulations in quantum mechanics
NEXT STEPS
  • Study the first-order correction methods in quantum mechanics using Sakurai's "Modern Quantum Mechanics"
  • Explore second-order Perturbation Theory examples in Griffiths' "Introduction to Quantum Mechanics"
  • Review Gasiorowicz's "Quantum Physics" for additional insights on PT
  • Practice calculating first-order corrections with specific quantum systems
USEFUL FOR

Students and researchers in quantum mechanics, particularly those seeking to deepen their understanding of Perturbation Theory and its applications in solving quantum systems.

ooleonardoo
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Homework Statement
Calculate the second-order corrections to energy for the following Hamiltonian matrix.
Use the degenerate perturbation theory. Consider 'b' as perturbation.
Relevant Equations
...
Of course, this question consisted of two parts. In the first part, we needed to calculate the first-order correction. It was easy. In all the books on quantum mechanics I saw, only first-order examples have been solved. So I really do not know how to solve it. Please explain the solution method to me. Thankful
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What are those books you mention? I would say Sakurai and probably a lot of other books do actually explain how to do PT to arbitrary orders.
 
Gaussian97 said:
What are those books you mention? I would say Sakurai and probably a lot of other books do actually explain how to do PT to arbitrary orders.
gasiorowicz, zettili , griffiths
The level of the book you mentioned is high for me. Do you know of any other book that explains this with an example?
 
Actually, Griffiths does have a discussion on second-order PT.
Anyway, can you show us how did you compute the first-order correction?
 

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