# Tagged Questions

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

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### Kepler Orbits: Small Perturbations->Elliptical Orbits

A group of my physics classmates and I have been stuck on this problem. We have tried a few approaches. The problem is to show that a body following a circular orbit, when given a small radial ...
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### Why is the energy shift due to a 'sagging' potential negative and independent of box size?

Consider a box of width $L$ and the composed of the following potential $$V(x)=\frac{V_0x(x-L)}{L^2}, x\in[0,L]$$ and $V(x)=\infty$ elsewhere. Using perturbation theory - with a square box as the ...
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### Time-dependent perturbation theory [on hold]

In time dependent perturbation theory there is a group of states having energies nearly equal to initial state.what will be time dependence of probability of finding system in any of such state? Plz ...
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### Particle creation through a time dependent Hamiltonian

We know that a time dependent Hamiltonian can create particles. We know this for instance from field theory in curved spacetime, where for instance in an expanding or contracting universe creation and ...
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### Book Recommendations on Perturbation Theory

I am interested in studying Quantum Electrodynamics and figure I should begin by learning Perturbation theory and Asymptotic expansions. If anyone could recommend some books, or starting points for ...
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### Griffiths Intro to QM Section 9.1.2: What type of approximation is he using here and what is the justification for it?

I really do not understand Griffiths logic in this section and was wondering if someone could help. This is basically a 1st order coupled system of ordinary differential equations but I haven't seen ...
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### Renormalization group resummation

I'm having trouble in understeanding a mathematical feature of RG, namely how it provides a way to resum the perturbation series and how that's defined mathematically. From a conceptual point of view ...
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### Degenerate perturbation theory

I don't understand the part about turning off the perturbation. What is meant by or what is he referring to when he says "upper" and "lower" states. Why must the "upper" state reduce to a combination ...
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### Why is stat mech involved in mean field theory?

Mean field theory involves approximating an interacting system by a non-interacting one, by replacing some operators with their expectation value. However, to my surprise, free energy is involved in ...
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### Peskin's book page 334 proof of $Z_1=Z_2$ to all orders in QED perturbation theory

Peskin in his QFT page 334 argued that $Z_1=Z_2$ to all orders in QED perturbation theory, but I couldn't understand his argument: ... With a generalization of the argument given there (section 7....
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### Why are the perturbation term in Zeeman effect not diagonalized?

In the case of weak field Zeeman effect (anomalous Zeeman effect) in hydrogen atom, the unperturbed Hamiltonian reads as $$H_0 = \frac{\hat{p}^2}{2m} + \frac{C_1}{r} + f(r)\mathbf{L}\cdot\mathbf{S}$$...
Schwartz's QFT book contains the following passage. To be precise, total derivatives do not contribute to matrix elements in perturbation theory. The term $$\epsilon^{\mu\nu\alpha\beta} F_{\mu\... 2answers 111 views ### Higher orders in perturbation theory I would like to compute an energy level up to many orders in perturbation theory. My difficulty right now is not in the calculation itself but in understanding the algebraic structure of the higher ... 1answer 64 views ### Derivative with respect to perturbation in QM The book "Introduction to Computational Chemistry" by Frank Jensen claims the following (Eq. 10.35): Let H(\lambda) = H_0 + \lambda V be a Hamiltonian parametrized by a perturbation strength of \... 0answers 52 views ### Is the Fermi golden rule really accurate for calculating the life time of an atomic level? In my impression, Fermi golden rule is routinely used in calculating the life time of an excited atomic level. But it is based on the first order perturbation theory, so it is not expected to be ... 2answers 449 views ### Why are many physicists trying to develop non-perturbative quantum theories? [closed] I would like to briefly know where (and why) does perturbation theory fail and why are physicists so desperate looking for non-perturbative theories. 1answer 45 views ### 1st order perturbation of energy for quantum harmonic oscillator [closed] I am trying to do part B of Griffiths QM 2nd edition problem 6.2 It asks to find the 1st order correction to the energy for a perturbation of a quantum harmonic oscillator where the new spring ... 0answers 83 views ### Relation between the reduced Green's function and the full Green's function Let us assume that we have some Hamiltonian and we know its spectrum$$H_0 \psi_n = E_n \psi_n .$$We define the Green's function in as$$ G(x,y,E) =\sum_m \frac{\psi_m^*(x)\psi_m(y)}{E-E_m},  and ...
In Griffiths Quantum Mechanics Example 6.1 on page 252, the problem is just a simple square well where the potential floor is raised from zero to $V_0$. Thus he states that the Hamiltonian for this ...