What is Perturbation theory: Definition and 263 Discussions
In mathematics, physics, and chemistry, perturbation theory comprises mathematical methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter
ϵ
{\displaystyle \epsilon }
. The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of
ϵ
{\displaystyle \epsilon }
usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction.
Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The field in general remains actively and heavily researched across multiple disciplines.
A quick question from a high school student,
In perturbation theory, what is to be done with the found energy correction? I'm working out the solution to an a/r+br potential and using br as the perturbation. I set up the integral and normalized, but what do I do with the expression that I'm...
if we know that the divergent series in perturbation theory of quantum field theory goes in the form:
\sum_{n=0}^{\infty}a(n)g^{n}\epsilon^{-n} with
\epsilon\rightarrow{0}
then ..how would we apply the renormalization procedure to eliminate the divergences and obtain finite...
I'm reading the Cohen-Tannoudji book and I found somthing I don't understand
in stationary perturbation theory.
the problem the Hamiltonian is split in the known part an the perturbation:
H=H_{o}+\lambda \hat{W}
H_{o}|\varphi_{p}^{i}\rangle=E_{p}^{o}|\varphi_{p}^{i}\rangle
(1)
and...
Hi,
I'm new to this subject, so bear with me. We consider the harmonic oscillator with a pertubation:
\hat{H}' = \alpha\hat{p}.
(What kind of a perturbation is that anyway, it's not a disturbance in the potential, what does it correspond to physically.)
Now I have to calculate the...
I have been studying Perturbation theory in my Quantum class but my professor has not really explained why physically it comes into play. The book says that perturbation theory is used to help come up with approximate solutions to the Schrodinger Equation. Is this analagous to how we use Fourier...
Can anybody explain what Griffiths means when he talks about "good eigenstates" in degenerate time-independent purturbation theory?
Mathematically, I know he is just talking about the eigen-vectors of the W matrix (where Wij = <pis_i|H'|psi_j>). But what do the eigen-vectors physically...
I was studying up on an aspect of perturbation theory, and I must have strained something (there's something about Hilbert spaces that I just can't get my head around...sorry, bad joke), because I have a really bad headache now.
I was wondering what a headache is, and how we get them. I know...
For the harmonic oscillator V(x) = \frac{1}{2}kx^2, the allowed energies are E_n=(n+1/2)h \omega where \omega = \sqrt{k/m} is the classical frequency. Now suppose the spring constant increases slightly: k -> (1 + \epsilon)k. Calculate the first order perturbation in the energy.
This is 6.2...
Hey there, I'm working on a perturbation theory problem, and I have no clue where to start in solving an infinite series.
It's an infinite square well with a delta function potential in the centre and I'm trying to find the 2nd order energy correction to Energy En. Anyway, what I've got is...
I have a problem where I should calculate the ground state eigenfunction of a particle in the box where the potential V(x)=0 when 0<x<L and infinite everywhere else with the perturbation V'(x)=\epsilon when L/3<x<2L/3.
I get that the total ground state eigenfunction with the first order...
can somebody help me to find an expression for the density contrast
(in fouruer space; delta_k) in a moving frame. Basically I am trying to
figure out how various quantities like power spectrum P(k) etc., will look in a uniformly moving frame .
we have a particle in an infinite one-dimensional square well potential
[V(x)=0 for 0<x<L and V(x) is infinite otherwise]
and introduce a small potential (perturbation) in the middle of the
square well potential. Then the first order energy correction
for the ground state is 100 times...
Here they go my doubts:
a)Could It be that a theroy that is not renormalizable in three or four dimension could it be renormalizaed in two?..i mean if depending on the dimension a theory is renormalizable or not...when it comes to gravity..in which dimension is renormalizable?.
b)When you...