Perturbation Theory: Calculating 1st-Order Correction

In summary, the conversation is about calculating the first-order correction in quantum mechanics and the availability of examples in textbooks. The speaker is asking for clarification on the solution method and mentions books by Sakurai, Gasiorowicz, Zettili, and Griffiths. They also express difficulty with the level of these books and ask for another resource. The other person in the conversation suggests Griffiths as a possible source and the speaker requests for a demonstration of the first-order correction calculation.
  • #1
ooleonardoo
2
0
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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  • #2
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.
 
  • #3
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?
 
  • #4
Actually, Griffiths does have a discussion on second-order PT.
Anyway, can you show us how did you compute the first-order correction?
 

What is perturbation theory?

Perturbation theory is a mathematical method used to approximate the solution of a problem that cannot be solved exactly. It involves breaking down the problem into simpler, solvable parts and then adding small corrections to improve the accuracy of the solution.

What is the first-order correction in perturbation theory?

The first-order correction in perturbation theory is the first term in a series of corrections used to improve the accuracy of the solution. It takes into account the small perturbations or deviations from the original problem and adds them to the original solution.

How is the first-order correction calculated?

The first-order correction is calculated by multiplying the first-order perturbation term by the unperturbed wavefunction. This is then added to the original unperturbed energy to obtain the corrected energy level.

What is the significance of the first-order correction in perturbation theory?

The first-order correction is significant because it provides a more accurate solution to a problem that cannot be solved exactly. It takes into account the small perturbations that may affect the original solution and improves its accuracy.

What are some applications of perturbation theory?

Perturbation theory is used in various fields such as quantum mechanics, classical mechanics, and fluid dynamics to approximate solutions to complex problems. It is also used in chemistry to calculate molecular properties and in engineering to analyze and design systems with small deviations from ideal conditions.

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