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# Questions tagged [perturbation-theory]

Perturbation theory refers to methods for understanding physical systems by treating them as small modifications to exactly solvable systems.

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### Occurances of integrals of the form $Z(\lambda) = \int g(x)e^{-\frac{f(x)}{\lambda}}dx$ (and perturbation techniques) [closed]

I am writing a review on perturbation techniques (actually hyperasymptotic techniques) for integrals of the form $$Z(\lambda) = \int g(x)e^{-\frac{f(x)}{\lambda}}dx,$$ where the interest is in the ...
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### Why this self-loop diagram is not included in $\phi^4$-theory of Peskin & Schroeder?

Consider a $2\rightarrow2$ scattering process in $\phi^4$-theory. On p. 326 in the book of Peskin & Schroeder, they consider the 3 1-loop corrections in the parenthesis: My question is: Why don't ...
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### Constant Density of States and Perturbation theory

Given a constant Density of States (DOS) corresponding to a one-electron hamiltonian, $\text{DOS}(\omega)=\dfrac{1}{2D} \chi_{[-D,D ]}(\omega),$ where $\chi$ is the indicator function, I want to know ...
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### Spring with oscillating support (Goldstein chapter 11, problem 2)

The problem: A point mass m hangs at one end of a vertically hung hooke-like spring of force constant k. The other end of the spring is oscillated up and down according to $z=a\cos(w_1t)$. By ...
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### Why can we add counterterms?

I'm having a hard time understanding why renormalized perturbation theory works. Why is it permissible to add counterterms to the Lagrangian? Terms which are often divergent themselves and carry ...
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### Time-dependent perturbation theory in a degenerate system

In the derivation of probability transition of time-dependent perturbation theory (see for example these notes, from Ben Simons from Cambridge University), I have only encountered treatments of non-...
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### Second Order Correction to the Perturbative Approximation of the Transition Amplitudes in RQM

I am studying Relativistic Quantum Mechanics from my professor's notes. When calculating the second order perturbative correction to the transition coefficient $T_{fi}$* in a scattering process by a ...
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### Proving the collapse of a many body system (Fetter and Walecka problem 1.2)

I was trying to solve the problem 1.2 from Quantum theory of many-body systems by A. Fetter and J. D. Walecka. I succeeded in the first part, obtaining the suggested formulation for the expectation ...
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### The stark effect on ground state [closed]

When considering the Stark Effect, we consider the effect of an external uniform weak electric field which is directed along the positive $z$-axis, $\vec E = E \hat z$, on the ground state of a ...
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### In perturbation theory, why can perturbed eigenfunctions be expanded into the basis set of the unperturbed eigenfunctions?

So I am studying non-degenerate time independent perturbation theory and I came across the derivation of the first order correction to the wavefunction. So the notes given to me affirm that the each "...
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### Using relativistic QFT to compute energy levels

I've taken a year of QFT so far, and although there seems to be a lot of attention paid to scattering amplitudes and decay rates and perhaps bound states, I view computing energy spectra as certainly ...
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### Can we show that the ground state of the He atom is a spin singlet rather than triplet?

The ground state of Helium atom is a state in which the space part of the wavefunction is symmetric and the spin part is antisymmetric under the exchange of the electrons. Therefore, the ground state ...
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### Path integral formulation of the density matrix ρ

In Feynman's Statistical Mechanics - A Set of Lectures, upon the introduction of the path integral, a series of approximations are made in order to calculate integrals. I am unsure how exactly to get ...
Let's say we have a quantum particle with mass $m$ in a 1-Dimensional box. The potential outside the box is infinite. Say that $n=2$, so that $|\psi|^2$ will have two maxima. How would the ...