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.

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  1. R

    How does Perturbation theory account for interactions in QED?

    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...
  2. P

    Hydrogen like atom, perturbation theory

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  3. V

    Perturbation theory to solve diff eq?

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  4. A

    Question on time-independent perturbation theory

    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...
  5. C

    Question on perturbation theory

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  6. P

    Diagonalizing a matrix using perturbation theory.

    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...
  7. E

    Perturbation theory - need a couple of articles

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  8. M

    Degenerate Perturbation Theory Wavefunction Correction

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  9. JK423

    Time-dependent perturbation theory

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  10. E

    Time-dependant perturbation theory & transitions

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  11. B

    Litle help with perturbation theory

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  12. T

    Degenerate perturbation theory help

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  13. M

    Degenerate Perturbation Theory: Operator commuting with Ho and H'

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  14. C

    Question about a scientific paper - Fluid Mechanics - Perturbation Theory

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  15. A

    Time independent perturbation theory (QM)

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  16. K

    A mathematical issue raised from perturbation theory

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  17. R

    Quick Q: First order perturbation theory derivation

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  18. A

    Is this interpretation logical? (Perturbation theory)

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  19. J

    Time dependent perturbation theory

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  20. J

    Perturbation theory and asymptotics

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  21. B

    First-order time-dependent perturbation theory on a Hydrogen atom

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  22. F

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  23. C

    Energy eigenfunctions in time-independent perturbation theory

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  24. A

    Question on Time-independent perturbation theory: I am confused

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  25. B

    Why do degenerate energy levels shift or split due to perturbation?

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  26. A

    Question about time limits of time-dependent perturbation theory

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  27. C

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  28. P

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  29. 1

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  30. A

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  31. J

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  32. P

    Mastering Perturbation Theory for Nuclear Engineering Students

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  33. M

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  34. N

    Perturbation theory / harmonic oscillator

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  35. G

    Perturbation theory question (in Quarks & Leptons)

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  36. C

    Energy shift using perturbation theory

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  37. J

    Where can I find perturbation theory formulas up to fourth order?

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  38. B

    Time-dependent perturbation theory question not a hard one

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  39. M

    Perturbation Theory description of Positronium

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  40. N

    Perturbation Theory: How Does Oscillation Amplitude Vary with Length?

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  41. S

    Degenerate perturbation theory

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  42. D

    Time dependant perturbation theory

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  43. J

    First order perturbation theory

    The potential of an electron in the field of a nucleus is: -Ze^2/(4 Pi Epsilon0 r) r > r0 -Ze^2/(4 Pi Epsilon0 r0) r <= r0 where r0 is the fixed radius of the nucleus. What is the pertubation on the normal hydrogenic Hamiltonian? Calculate the change in energy of the 1s state to the first...
  44. MathematicalPhysicist

    Another 2 questions in perturbation theory.

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  45. MathematicalPhysicist

    Calculating Electron Energy Shift with Perturbation Theory

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  46. N

    Time-dependent perturbation theory

    Hi all Please look at this link (Search for the phrase "The quantum state at each instant can be expressed as a linear combination of the eigenbasis"): http://en.wikipedia.org/wiki/Perturbation_theory_%28quantum_mechanics%29 If we write the wavefunction for the perturbed system as a...
  47. A

    How Does Degenerate Perturbation Theory Apply to Matrix Elements?

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  48. Z

    Perturbation Theory: 2D Harmonic Oscillator & Energy Levels

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  49. J

    Perturbation theory in 3D potential

    Homework Statement Consider a quantum particle of mass m in a 3-D harnonic potential with frequency \omega and it experiences a perturbation H_{1}=az^{2} a. Determine the effect of H_{1} on the 1st exicted level of the system ( at the 1st order perturbation) b. what happen to L^{2} and...
  50. L

    Perturbation Theory: Square Well & Energy Levels

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