Ví dụ về việc sử dụng Perturbation theory trong Tiếng anh và bản dịch của chúng sang Tiếng việt
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Hence the name"perturbation theory".[9].
Perturbation theory finds(at worst) the locally shortest path.
His explanation was based on the second-order perturbation theory.
But perturbation theory assumes we also have⟨ n|.
What is it that is"symmetry-adapted" about symmetry-adapted perturbation theory?
Physicists must apply perturbation theory to obtain a series of approximated solutions.
It improves on the Hartree- Fock method by adding electron correlation effects by means of Rayleigh-Schrödinger perturbation theory(RS-PT), usually to second(MP2), third(MP3) or fourth(MP4) order.
This is why this perturbation theory is often regarded as Rayleigh- Schrödinger perturbation theory.
The nice thing about this is that at each order in perturbation theory there is only one diagram.
Paul Dirac developed perturbation theory in 1927 to evaluate when a particle would be emitted in radioactive elements.
As we shall discuss in some detail in Chapter 12, the mathematical framework of string theory is so complicated that physicists have been able to performonly approximate calculations through a formalism known as perturbation theory.
Many of the ab initio quantum chemistry methods use perturbation theory directly or are closely related methods.
Time-independent perturbation theory is one of two categories of perturbation theory, the other being time-dependent perturbation(see next section).
However, further studies by Felix Bloch with Arnold Nordsieck,[4] and Victor Weisskopf,[5] in 1937 and 1939, revealed that such computationswere reliable only at a first order of perturbation theory, a problem already pointed out by Robert Oppenheimer.
On the more advanced side, mathematical perturbation theory is also sometimes used(a working is shown for this particular example here).
The gradually increasing accuracy of astronomical observations led to incremental demands in the accuracy of solutions to Newton's gravitational equations, which led several notable 18th and 19th century mathematicians, such as Lagrange and Laplace,to extend and generalize the methods of perturbation theory.
In time-independent perturbation theory the perturbation Hamiltonian is static(i.e., possesses no time dependence).
Perturbation theory was investigated by the classical scholars- Laplace, Poisson, Gauss- as a result of which the computations could be performed with a very high accuracy.
A critical feature of the technique is a middle step thatbreaks the problem into"solvable" and"perturbation" parts.[1] Perturbation theory is applicable if the problem at hand cannot be solved exactly, but can be formulated by adding a"small" term to the mathematical description of the exactly solvable problem.
Perturbation theory also fails to describe states that are not generated adiabatically from the"free model", including bound states and various collective phenomena such as solitons.
He completed a doctorate on quantum perturbation theory at the University of California, Berkeley, in 1981, and joined the faculty at Caltech.
Perturbation theory is a very useful tool for studying the physics at weak coupling, and most of our current understanding of particle physics and string theory is based on it.
The expressions produced by perturbation theory are not exact, but they can lead to accurate results as long as the expansion parameter, say α, is very small.
Perturbation theory leads to an expression for the desired solution in terms of a formal power series in some"small" parameter- known as a perturbation series- that quantifies the deviation from the exactly solvable problem.
Time-independent perturbation theory was presented by Erwin Schrödinger in a 1926 paper, shortly after he developed his theories in wave mechanics.
Perturbation theory also fails to describe states that are not generated adiabatically from the"free model", including bound states and various collective phenomena such as solitons.[citation needed] Imagine, for example, that we have a system of free(i.e. non-interacting) particles, to which an attractive interaction is introduced.
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one.
Computers have also been used to carry out perturbation theory calculations to extraordinarily high levels of precision, which has proven important in particle physics for generating theoretical results that can be compared with experiment.
The earliest use of what would now be called perturbation theory was to deal with the otherwise unsolvable mathematical problems of celestial mechanics: for example the orbit of the Moon, which moves noticeably differently from a simple Keplerian ellipse because of the competing gravitation of the Earth and the Sun.[2].
The standard exposition of perturbation theory is given in terms of the order to which the perturbation is carried out: first-order perturbation theory or second-order perturbation theory, and whether the perturbed states are degenerate, which requires singular perturbation. .