Perturbation Theory: Calculating 1st-Order Correction

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The discussion focuses on calculating the first-order correction in perturbation theory, with participants noting that many quantum mechanics textbooks primarily cover first-order examples. Some recommended texts include Sakurai, Gasiorowicz, Zettili, and Griffiths, with Griffiths also addressing second-order perturbation theory. A participant expresses difficulty with the complexity of these texts and seeks simpler resources or examples. The conversation emphasizes the need for clear explanations and examples to understand perturbation theory better. Overall, the thread highlights the challenge of finding accessible learning materials for higher-order corrections in quantum mechanics.
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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?
 

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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