In science and engineering, one often solves a perturbed model representing; an ODE, a PDE, an algebraic equation...
Are we deliberately perturbing the equations and solve or what is the physical meaning?
It may also occur during Lab based practical experiments or what?
How does it affect the model or equation?
So many thanks!
Perturbation means disturbance in the state variables of the system. In mathematical sciences, we do perturb the parameters/variables to check for the stability of the system.
In physical sciences, these perturbations can be either natural or forced.
Let me explain it with two examples:
1. There is a pendulum and initially it is in steady condition. If we perturb the pendulum, it will be in oscillatory motion and after some time it will again come to the steady condition.
2. The flow of electricity in transmission lines experience fluctuations when there is a sudden change in frequency. The electrical equipments are designed to sustain a range of frequency and beyond that, they may get damaged.
There can be several other examples to understand this phenomenon like the flow of fluid in a tube/ pipe; noise in sound waves etc. So mathematicians, create some hypothetical situations by perturbing the variables and check whether the system will be able to sustain these or not and up to what extent.
So In physical sciences, perturbation is nothing but a sudden disturbance in any state variable.
Hi Dr Tekle Gemechu . Simply it means modified mathematically for the correction .
The concept of perturbation is used often and in many different contexts with different meanings. One typical in applied mathematics is that in which some variable u is considered as the sum u=U+u' of a 'reference' part U (usually assumed to satisfy some simplified form of the general underlying equations) and a 'perturbation' part u' (usually assumed to be such that |u'|
In
https://www.quora.com/What-can-be-the-physical-interpretation-of-the-fact-that-the-second-order-correction-to-the-ground-state-energy-of-a-system-for-a-time-independent-perturbation-is-always-negative
we find the following interesting answer
Of course the terms in perturbation theory have physical meaning... The first order correction is the energy your reference (zeroth order) wave function feels under the true Hamiltonian of the system (thus it is variational for the ground state). The second order correction to the energy is the first term that includes a correction to the wave function. So it has to decrease the ground state energy of the system, as it corrects the wave function to be more similar to the ground state than the reference Hamiltonian’s ground state wave function.
-In general, when you assert that something is just a mathematical artifact with no physical significance there's a good chance that you are wrong. There are an enormous number of examples where the partitioning of the hamiltonian in perturbation theory grants physical insight into quantum mechanics problem. A few examples from chemistry:
1. Moller Plesset Theory - where the 0th order term gives the energy of the Fock operator, the first order correction gives the energy of the self-consistent field wavefunction in the true Hamiltonian, and the second order term reflects the first attempt at capturing electron correlation
2. Symmetry Adapted Perturbation Theory - a double perturbation theory where the partitioning of the Hamiltonian is such that the electron correlation and the interaction between molecules is treated perturbatively. This naturally breaks the interaction energy into electrostatics, exchange, induction, and dispersion contributions, as well as how these terms couple at various orders (i.e. Exch-Ind ).
3. Frontier Molecular Orbital Theory - A largely qualitative (i.e. PHYSICAL) treatment of molecular reactivity where second order perturbation theory is truncated to include only the dominant terms: HOMO-LUMO interactions between the reactants
Dear,
George Stoica and co-author (Cristina Stoica)
and
Maged Gumaan Bin-Saad
too many thanks for the reference links!
Thank you all!
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