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

learn more… | top users | synonyms

0
votes
0answers
52 views

Perturbation theory, eigenvalues and eigenvectors for degenerate case (1st order)

I was trying to understand the perturbation theory, but I was lost in the notation... I have understood that I have to identify the unperturbed kets that are degenerated and find the matrix $V$, ...
2
votes
2answers
55 views

What justifies the perturbative expansion in chiral perturbation theory?

The Lagrangian of chiral perturbation theory is ordered following a momenta power counting scheme, having terms at leading order (which is two 2 $O(p^2)$) next to leading order ($O(p^4)$) and so on. ...
0
votes
0answers
41 views

Is this solvable? Time-dependent perturbation theory

The question is A hydrogen atom is placed in a time-dependent homogeneous electric field given by $$ \varepsilon(t) = \varepsilon_0(t^2 + \tau^2)^{-1} $$ where $\varepsilon_0$ and ...
0
votes
1answer
60 views

Lippmann-Schwinger equation and $T$ expansion

Lippmann-Schwinger equation, in operator form, is: $$ T=V+V\frac{1} {E-H_0+i \hbar \varepsilon} T=:V+V\Theta_0T, $$ where $H_{tot}=H_0+{V}$ is the hamiltonian ($H_0$ is the free particle hamiltonian ...
1
vote
0answers
11 views

Definition of linear response kernel in terms of wavefunctions (Parr/Yang)

I'm trying to understand the derivation of the linear response kernel in Parr/Yang's "Density-functional theory of atoms and molecules". First some background information: We look at a system of $N$ ...
0
votes
0answers
18 views

If we considered chiral perturbation theory with coplex $\phi$-s, wold the next lo leading order renormalization $\gamma$-s change?

The Lagrangian of chiral perturbation theory (with two quark flavors) is written using the following matrix $U$ $$U=e^{i\sigma^i\phi_i/f}$$ where $\sigma^i$ are the Pauli matrices, $\phi_i$ are three ...
0
votes
0answers
14 views

Transition from the second excited state to the ground state in 3d oscillator [on hold]

The problem: 3d harmonic oscillator is in a second excited state. Suddenly a perturbation is applied which depends only on the length of the position vector $|\vec{r}|$. Can the oscillator fall into ...
7
votes
2answers
307 views

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 ...
2
votes
1answer
53 views

Perturbation theory in second quantization

I am dealing with electron/phonon interaction in QM. In particular, given the Hamiltonian of a solid, $$H=H_{el}+H_{ion}+H_{el-ion}$$ we have that the el-phonon Hamiltonian is treatened ...
0
votes
0answers
11 views

Limitation of Rytov approximation for turbulence

I have been working through the textbook "Laser Beam Propagation through Random Media" by Andrews and Phillips and have arrived at an interesting dilemma. For a second-order perturbation in the Born ...
0
votes
0answers
16 views

Bound states and corresponding elementary fields

Let's have some bound state, like positronium or meson. I need to calculate an amplitude of process which involves bound state in in- or out-state. Is it necessary to introduce corresponding ...
2
votes
1answer
26 views

Proton spin independent fine structure “Hamiltonian” $W_f$

To find the perturbation correction (fine structure) in the case of a degenerate energy $E_n^0$, we can diagonalize the operator $W_f^n$, the restriction of $W_f$ to the eigen-space associated to ...
1
vote
3answers
53 views

Is the perturbation Hamiltonian an observable?

In fine structure calculation we use the perturbation theory. The basic Hamiltonian $H_0$ is perturbed as: $H = H_0 + W$ First, the basic problem assume that $H_0$ is an observable. That allows to ...
3
votes
2answers
521 views

Second order degenerate perturbation theory

What is a good resource to learn about higher degree degenerate perturbation theory - one that involves mathematics that isn't much more advanced than first order perturbation theory? I've looked ...
1
vote
0answers
31 views

Quantum perturbation theory recommendations

What are some concise resources, in particular, online resources, for perturbation theory in quantum mechanics? I want something like a crash course to perturbation theory in quantum mechanics that is ...
0
votes
1answer
110 views

Time evolution of two orthogonal states in Time Dependent Perturbation Theory

Given the two orthogonal states for $H_0$ , $|n(t)>_I, |m(t)>_I$, in the interaction picture, we want to find the probability of transforming from one to the other after time t, aka: $ \ (1) \ ...
1
vote
1answer
76 views

Effective hamiltonian for the second-order degenerate perturbation theory

I'm currently trying to figure out the way we arrive to the Hamiltonian of a topological insulator. In an article by Xiao-Liang Qi (arXiv: http://arxiv.org/abs/1005.1682) in a process of arriving to ...
6
votes
2answers
262 views

Is WKB really applicable for the ground state?

It seems that WKB is applicable for a given $E$ if and only if $\hbar$ is sufficiently small. Or in other words, WKB is applicable if and only if the quantum number is large enough. Is this ...
3
votes
1answer
115 views

Estimating volume of moduli space of genus-g Riemann surface with n marked points

I wanted to know how can I estimate the volume of the moduli space of a Riemann surface of genus $g$ and having $n$ marked points. I am reading some old string theory papers which discuss divergences ...
3
votes
1answer
185 views

Hartree-Fock correction to $e$-$e$ interaction

The corrections to the energy per electron in a jellium model (uniform distribution of positive ion charge approximation to the regulated long range order ionic array) is given by (in units of Ry) ...
2
votes
1answer
174 views

Do perturbative renormalization groups help one understand when perturbation theory can be used in general?

If, as I asked in this question, a relevant operator in a renormalization group transformation can't be used in a perturbative expansion since it becomes large as the transformations are applied, does ...
2
votes
1answer
121 views

How was this one probability amplitude derived by Mattuck?

I'm reading A Guide to Feynman Diagrams in the Many-Body Problem by Richard D. Mattuck (2nd edition). You can look at the relevant pages here. On page 45, he presents a formula for $D_t c_p(t)$. ...
2
votes
0answers
40 views

How is translational symmetry related to Fourier decomposition?

The book (The Cosmic Microwave Background By Ruth Durrer) about cosmological perturbations says that because of translational symmetry of the background at a constant time, we can decompose our ...
1
vote
0answers
33 views

Corrections in Perturbation theory

Is there a way to construct a bound on the perturbative corrections to a problem in perturbation theory? For example, if I have the standard 1st order correction to the eigensolutions of a problem ...
5
votes
4answers
1k views

How to decide whether one can use perturbation theory in QM?

In QM, it is said that perturbation theory can be used in the case in which the total Hamiltonian is a sum of two parts, one whose exact solution is known and an extra term that contains a small ...
2
votes
0answers
59 views

Rigorous Proof of General Relativity's Non-renormalizability?

The answer to this question and the comments on it implies that general relativity has not been rigorously shown to be non-renormalizable for all loop diagrams -- only shown for two loops. However, ...
12
votes
2answers
609 views

Small oscillations of heavy string

I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points. First of all I wrote down this Lagrangian: ...
2
votes
0answers
38 views

Perturbation in Linear Response Theory (classical formalism)

A N-particles system is described by the following Hamiltonian $$H=H_0+H'(t)$$ where $H_0$ is the unperturbated Hamiltonian and $H'(t)$ is the perturbation $$H'(f)=-A\cdot\mathcal{F}(t)$$ written as ...
1
vote
0answers
63 views

How do the renormalization enter the actual amplitude calculation in QFT?

I have studied QFT from Peskin and Schroeder and from a few other books and lectures and I think I understand the procedure of renormalizing various parameters in the Lagrangian like mass, coupling ...
1
vote
1answer
69 views

Kubo formula for general observables

In the wiki page about Kubo formula, the expectation of some observable under weak time-dependent perturbation is derived. However, from my point of view, some crucial steps are missing. I did the ...
7
votes
0answers
353 views
1
vote
0answers
28 views

Expectation value in spin-orbit coupling

So I was just trying a question where it asked to find the Energy shift due to a spin-orbit coupling Hamiltonian to first order using perturbation theory. The Hamiltonian is $$H_{LS} = ...
1
vote
0answers
33 views

What is a diffusionless fluid?

I'm taking a course in astrophysical fluid dynamics and have come across a problem involving "small diffusionless disturbances" of a fluid. Based on the nature of the course I expect the examiner to ...
3
votes
1answer
82 views

What really are perturbation expansions?

I'm unsure if this question belongs here or at Math.SE, but since I've got to it by reading some articles about Physics I'm going to post it here anyway. In this particular article (Theoretical ...
1
vote
1answer
111 views

Perturbations in linear response theory

I've been working on applications of linear response theory to condensed matter systems, and I've got quite far into the literature on the subject. However, there is an identity which seems to be ...
0
votes
0answers
19 views

How should I interpret degenerate $\pm m_j$ states under the Stark effect?

I'm thinking about the Stark effect in Alkalis where fine structure is important (Cs, Rb, etc). The Stark effect doesn't lift the degeneracy of the $\pm m_j$ states. So should I interpret a state ...
6
votes
1answer
63 views

Post-Minkowskian expansion of some quantities in Post-Newtonian theory

I'm studying Post-Newtonian theory on the book "Gravity" by Poisson and Will and I found a few formulas that I can't obtain by myself. I'm pretty sure it must be quite simple, but can't find the right ...
2
votes
0answers
62 views

Scalar QED perturbation theory [closed]

Where can I find material about scalar QED? Renormalization, scattering matrix, perturbation theory, etc...
10
votes
1answer
164 views

LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free ...
4
votes
1answer
101 views

Fermi Golden Rule

First order time dependent perturbation theory tells us that under the influence of a perturbation $Ve^{i\omega t}$, a system that started in the state $|n\rangle$ at time $t=0$ has probability ...
2
votes
1answer
428 views

Coupled Oscillators

This is an exercise of my last exam. Since I couldn't find anybody who solved it or knows how to, it would be really nice if somebody could tell me if my thoughts on it go into the right direction. ...
1
vote
0answers
26 views

Variational principle perturbation

I am trying to learn 2D SHO and free particle variational principles. However, I came across a perturbation like so: $Ax^2y^2$. The particle is simple harmonic in $x$ and a free particle in $y$? I'm ...
1
vote
0answers
27 views

Second-order correction in Quantum-Confined Stark effect

In the wikipedia article, there is a second-order correction in the Quantum-Confined Stark Effect. I could not understand how it was solved. I did not understand the meaning of 2(0) and 1(0) and how I ...
3
votes
2answers
130 views

Perturbation theory in quantum harmonic oscillator [closed]

This question concerns the quantum harmonic oscillator: (a)Express the operator $\hat B = \hat x \hat p + \hat p \hat x + \hbar$ in terms of $\hat a_{\pm}$ and $\hbar$ (b)Write the matrix ...
1
vote
2answers
207 views

How to tell the order of a Feynman diagram?

How can we know the order of a Feynman diagram just from the pictorial representation? Is it the number of vertices divided by 2? For example, I know that electnro-positron annihilaiton is first ...
2
votes
0answers
150 views

Perturbation theory : quadratic external field

I'm trying to derive the explicit form of S-matrix of an interaction Hamiltonian $$H' = \frac{1}{2} \lambda \left[ \int d^3 x \rho({\vec x}) \phi({\vec x}, t)\right]^2\tag{1}$$ Even though the ...
9
votes
1answer
881 views

Kramers-Kronig relations for the electron Self-Energy Σ

I'm currently studying an article by Maslov, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when ...
0
votes
0answers
40 views

Linear Perturbation theory in General Relativity, what to do with products of derivatives?

I'm trying to do a problem in which I am given the Einstein tensor for the following metric: $$ ds^2 = -e^{2\Phi}(d{x^0})^2 + e^{2\Psi}\delta_{ij}dx^idx^j, $$ And then asked to find the Einstein ...
0
votes
1answer
59 views

Definition of “nonlinear” in the context of perturbation of gravity

What exactly is the definition of a nonlinear perturbation when applied to a background spacetime metric? I have seen so called "linear perturbations" which look like $$ds^2 = -(1+2\Phi)dt^2 ...
1
vote
0answers
56 views

Applicability of perturbation theory

Consider some system in some initial state $|k^{(0)}\rangle$. The probability that such a state makes a transition to some other state $|m^{(0)}\rangle$ can be computed to various orders in time ...