Perturbation Definition and 426 Threads

It is well known due to the famous argument by Dyson that the perturbation series for quantum electrodynamics has zero radius of convergence. Dysons argument essentially goes like that: If the power series in α had a finite (r>0) radius of convergence it also would converge for some small...

hi,my friends.I have a perturbation operator problem. v=ezE; why this formula is right?how to deduce it?a is bohr radius. thank you!

Not sure if anyone has any experience with chiral perturbation theory, but I'm trying to see what all of the vertices are for interactions with a single Z boson. I've looked at the lagrangian up to order p^4 so far, and it seems that the Z only interacts with charged pions/kaons. I'm using...

Homework Statement Homework Equations E_{1}=<ψ_{1}|V(r)|ψ_{1}> The Attempt at a Solution That is equal to the integral ∫ψVψd^3r So I'll just perform the integral, correct ? But r is not constant here right? So, I' ll keep it inside the integral? How should I continue? Please...

If I have V(x)=\frac{1}{2}m\omega^{2}x^{2} (1+ \frac{x^{2}}{L^{2}}) How do I start to solve for the hamiltonian Ho, the ground state wave function ?? Calculate for the energy of the quantum ground state using first order perturbation theory?

From the tensor, ##\bar{h}^{ij}=h^{ij}-1/2\eta^{ij}h## Where, h=##h^i_i##, Prove that ##\bar{h}=-h##, Where, ##\bar{h}=\bar{h}^i_i##

Hello again, I also have another question, somewhat related to my previous, on the topic of the Klein-Gordon equation but treating the mass as a perturbation. The feynman diagram shows the particular interaction: I believe the cross is the point of interaction via the perturbation...

Hey, I'm struggling to understand a number of things to do with this derivation of the scattering amplitude using time dependent perturbation theory for spinless particles. We assume we have some perturbation 'V' such that : \left ( \frac{\partial^2 }{\partial t^2}-\triangledown ^2 +...

$$ \frac{d^2x}{dt^2} + x + \epsilon\frac{dx}{dt}\left[1 - \left(\frac{dx}{dt}\right)^2 + \beta\left(\frac{dx}{dt}\right)^4\right] = 0,\quad\quad\epsilon\ll 1, $$ Is there a smart way to do this problem? It will take forever to do directly.

This is in relation to multi-scale perturbation techniques. $x''+\epsilon f(x,x') + x = 0$ $f(x,x') = (x^2-1)x'$ \begin{alignat*}{3} f\left(x_0 + \epsilon x_1 + \cdots , \left(\frac{\partial}{\partial t} + \epsilon\frac{\partial}{\partial T}\right)(x_0 + \epsilon x_1 + \cdots)\right) & = &...

Homework Statement If E1≠E2≠E3, what are the new energy levels according to the second-order perturbation theory? Homework Equations H' = α(0 1 0) (1 0 1) (0 1 0) ψ1= (1) (0) (0) ψ2= (0)...

I just want to make sure that I am doing some things correctly. I'll be using http://www.physics.umd.edu/courses/Phys741/xji/chapter5.pdf from about 5.64 on. The kinetic term : \frac{f^2}{4} Tr[D_{\mu} \Sigma D^{\mu} \Sigma^{\dagger}] Now if I want to expand this out, as \Sigma =e^{i...

in the infinite well with small potential shown in the attachment. I calculated the total energy by using the time independent Schrodinger equation and adding the correction energy to the equation of the slope k=(Vo/L)x. E=h^2/8mL^2 +∫ ψkψ dx ψ=√(2/L) sin⁡(∏/L x) when integrating ∫...

in the infinite well with small potential shown in the attachment. I calculated the total energy by using the time independent Schrodinger equation and adding the correction energy to the equation of the slope k=(Vo/L)x. E=h^2/8mL^2 +∫ ψkψ dx ψ=√(2/L) sin⁡(∏/L x) when integrating ∫...

Question: obtain 2-term expansions for the roots of x^3+x^2-w=0 , 0<w<<1. I assumed an expansion of the form x=a+bw+... and from this obtained a=-1, b=1 as one solution. How do I work out the form of the other 2 expansions? Thanks.

Homework Statement The deuteron ground state is made up of l = 0 and l = 2 states; a)Show this mixture cannot be an eigenstate of a central potential Hamiltonian b)Using first-order time independent perturbation theory, argue the potential must contain a term proportional to some combination of...

I'm rather stuck on this problem. I seem to be having issues with the simplest things on this when trying to get started. Homework Statement There is a particle with spin-1/2 and the Hamiltonian H_0 = \omega_0 S_z. The system is perturbed by: H_1 = \omega_1 S_x e^{\frac{-t}{\tau}}...

I need some example driven learning material for my "singular perturbation" class. Someone help me please.

As expected, my textbook and teacher are both lacking clear, concise examples for me to work with, so would someone point me to early examples within the context of "perturbation techniques", preferably with WORKED OUT solutions for cross reference? thanks

Ok so I have a classic particle in a box problem. If a particle in a box, the states of which are given by: ψ = (√2/L) * sin(nπx/L) where n=1,2,3... is perturbed by a potential v(x) = γx , how do I calculate the energy shift of the ground state in first order perturbation I'm guessing that...

I want to know about relativistic correction to perturbation. I searched but failed to find any teaching on this topic. Is it true that we just need to replace the non-relativistic Hamiltonian perturbation terms with the relativistic ones while leaving the perturbation formulae unchanged...

Hi all, On p.327 in my second edition of Peskin and Schroeder, I have an expression for the one loop correction to the 4-point amplitude of phi^4 theory: i\mathcal{M}=-i\lambda - \frac{i \lambda^2}{32 \pi^2}\text{[Complicated integral]} Mathematica can do the integral for me, and all that...

I apologize that this is rather specific, but hopefully enough people have used Goldstein. I have a basic grasp of action-angle variables, and I'm going through the time-independent perturbation theory section in Goldstein (12.4). In this section we seek a transformation from the unperturbed...

Classical Perturbation Theory--Time Dep. vs. Time Indep (Goldstein). Hi, I'm going through Goldstein, and I'm a little confused on the distinction between time dependent and time independent perturbation theory. In section 12.2, they do the case of a simple harmonic perturbation on force...

Homework Statement How does the energy change (negative, positive or no change) in the HOMO-LUMO transition of a conjugated polyene where there are 5 double bonds when a nitrogen is substituted in the center of the chain? The substitution lowers the potential energy in the center of the box...

It is easy to understand for example how Jupiter pulls (perturbation) the orbit of the Earth more elliptic. But after a certain period the orbit will again be more circular. How does that (the opposite) work ?

can anyone hlep me with this qustion ? Consider the equation ε x^3 + x^2 - x - 6 = 0 ,ε > 0. (1) 1. Apply a naive regular perturbation of the form x~^{0}_{∞}Ʃ xn εn as ε→0+ do derive a three-term approximation to the solutions of (1). 2. The above perturbation expansion...

the spin orbit coupling removes the degeneracy but not completely, should we still use the degenerate perturbation theory. is it because of relativistic corrections? Thanks!

The following comes from Landau's Statistical Physics, chapter 32. Using a Hamiltonian \hat{H} = \hat{H}_0 + \hat{V} we get the following expression for the energy levels of a perturbed system, up to second order: E_n = E_0^{(0)} + V_{nn} + \sideset{}{'}{\sum}_m \frac{\lvert...

Hi all, I have a question about perturbation theory and the fine structure constant. Consider an electron moving through the vacuum - this wil induce vacuum polarization, and (if I understand correctly) perturbation theory can be used to analyze the situation. My question is essentially: if...

hey, say you have a infinite potential well of length L, in the middle of the well a potential step of potential V and length x. Inside the well is a particle of mass m. why are the first order energy corrections large for even eigenstates compared to odd ones? also, say well...

i see people discussing the convergence radius of a perturbation series in the literature i am really baffled generally, one can only get the first few coefficients of a perturbation series that is, the perturbation series is not known at all how can one determine the convergence...

Homework Statement I'm looking at the 1d harmonic oscillator \begin{equation} V(x)=\frac{1}{2}kx^2 \end{equation} with eigenstates n and the time dependent perturbation \begin{equation} H'(t)=qx^3\frac{(\tau^2}{t^2+\tau^2} \end{equation} For t=-∞ the oscillator is in the groundstate...

The singularity theorems apply to situations away from exact symmetry ... away from Schwarzschild solution or Friedmann solutions for example. There are a number of accounts of the singularity theorems but none addressing the problem of proving a 'trapped set' still persists after slight...

The problem given is a perturbation on the two dimensional harmonic oscillator where the perturbation is simply: H'=-qfy. It seems that all of the elements of the matrix H' are zero and so constructing a diagonal matrix in the subspace is eluding me. Any ideas?

Hello guys. I was told to prepare a presentation on perturbed Einstein's field equation by my advisor. I got some of the things I needed to start with in the Weinberg's Cosmology book but it was not enough. Can anyone please tell me a book or anything with information on metric perturbation? Thanks

time-independent, non-degenerate. I am referring to the following text, which I am reading: http://www.pa.msu.edu/~mmoore/TIPT.pdf On page 4, it represents the results of the 2nd order terms. In Eqs. (32), (33) and (34) I don't understand the second equality, i.e. basing on which formula he has...

Hi I am reading about Degenerate Perburbation Theory, and I have come across a question. We all know that the good quantum numbers in DPT are basically the eigenstates of the conserved quantity under the perburbation. As Griffiths he says in his book: "... look around for some hermitian...

Many of you stated how ad hoc is QFT as the field is supposed to be non-interacting yet how could they get an incredibly accurate value of calculated magnetic moment of the electron of value 1.0011596522 compared to measured 1.00115965219 with accuracy to better than one part in 10^10, or...

Hi all ! I need some help Homework Statement The nucleus of an hydrogen-like atom is usually treated as a point charge Ze. Using the first order perturbation theory, estimate the error due to this approximation assuming that the nucleus is a sphere of radius R with a uniform charge...

Homework Statement Consider a system with states |i> (with energy Ei) and |f> with energy eF) AND A PPERTURBATION OF THE FORM w(t)=wcosωt i) WHAT IS THE PROBABILITY P(t) FOR A TRANSITION BETWEEN |i> AND |f> ? ii)FOR WHICH VALUE OF ω IS THE PROBABILITY MAXIMAL ?GIVE THE PROBABILITY IN THIS...

Hi all, I have a tricky problem in pertubation theory. I have a function: f(\vec{r}) = P(\vec{r}) + \left( B(\vec{r}) + b(\vec{r}) \right)^2 where b(\vec{r}) is a small perturbation and is equal to 0 when P(\vec{r}) = 0 Now, to solve the equation \nabla f(\vec{r}) = 0 for b(r) is...

Hi all. I have been thinking about a very simple question, and I am a little confused. We know from time-independent perturbation theory that if the system is perturbed by the external perturbation λV which is much smaller compared to the unperturbed hamiltonian H0, we can write the ground state...

Hi there!I'm working on a physics problem where there is a liquid droplet (not necessarily spherical) on a plane. Transforming from cylindrical coordinates to bispherical: (r,\phi,z)\mapsto (\xi,\eta,\varphi;a) such that r={\frac {a\sin \left( \eta \right) }{\cosh \left( \eta \right) +\cos...

Homework Statement The potential of a simple harmonic oscillator of HF has the following form \frac{1}{2}kx^2 + bx^3 + cx^4 The first part of the problem involved finding expressions for the first-order energy corrections for the first three states, which I found below. Basically the x3 term...

Hello! I am answering a problem which involves spins in the hamiltonian. The hamiltonian is given by H = B(a1Sz^(1) + a2Sz^(2)) + λS^(1)dotS^(2). The Sz^(1) and Sz^(2) refers to the Sz of the 1st and 2nd spins respectively. B is the magnetic field and the others are just constants. The...

Hey everyone, I'm studying quantum mechanics from Griffiths (Introduction to Quantum Mechanics, 2nd edition), and I'm puzzling over his derivation of the nth order corrections to the energies and corresponding eigenstates for a perturbed Hamiltonian. The steps that are outlined in Griffiths...

Homework Statement This problem arises from the following ODE: \epsilon y'' + y' + y = 0, y(0) = \alpha, y(1) = \beta where 0 < x < 1, 0 < \epsilon \ll 1 Find the exact solution and expand it in a Taylor series for small \epsilon Homework Equations I guess knowing the Taylor...

Homework Statement Consider the following Hamiltonian. H=\begin{pmatrix} 20 & 1 & 0 \\1 & 20 & 2 \\0 & 2 & 30 \end{pmatrix} Diagonalize this matrix using perturbation theory. Obtain eigenvectors (to first order) and eigenvalues (to second order). Ho=\begin{pmatrix} 20 & 0 & 0 \\0 & 20 & 0...

Homework Statement "A ball is tossed upwards with speed V_0. Air resistance is -mkv^2 and there's gravity too. Find the the time it takes the ball to reach the maximum height. Do not solve the equation of motion exactly. Use the perturbation method on the equation of motion. Solve the equation...