Search results
Results from the WOW.Com Content Network
In astronomy, perturbation is the complex motion of a massive body subjected to forces other than the gravitational attraction of a single other massive body. [1] The other forces can include a third (fourth, fifth, etc.) body, resistance, as from an atmosphere, and the off-center attraction of an oblate or otherwise misshapen body.
Perturbation or perturb may refer to: . Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly; Perturbation (geology), changes in the nature of alluvial deposits over time
In other words, no longer denotes the exact variation of the eigenvalue but its first order approximation. As the matrix is symmetric, the unperturbed eigenvectors are M {\displaystyle M} orthogonal and so we use them as a basis for the perturbed eigenvectors.
Perturbation theory is an important tool for describing real quantum systems, as it turns out to be very difficult to find exact solutions to the Schrödinger equation for Hamiltonians of even moderate complexity.
In linear algebra, Weyl's inequality is a theorem about the changes to eigenvalues of an Hermitian matrix that is perturbed. It can be used to estimate the eigenvalues of a perturbed Hermitian matrix.
A perturbed problem whose solution can be approximated on the whole problem domain, whether space or time, by a single asymptotic expansion has a regular perturbation.Most often in applications, an acceptable approximation to a regularly perturbed problem is found by simply replacing the small parameter by zero everywhere in the problem statement.
In other words, the two pressure perturbations reinforce one another in the fast mode, but oppose one another in the slow mode. As a result, the fast mode propagates at a faster speed than the slow mode. [2] The group velocity v g ± of fast and slow magnetosonic waves is defined by
In physics and other fields of science, one frequently comes across problems of an asymptotic nature, such as damping, orbiting, stabilization of a perturbed motion, etc. Their solutions lend themselves to asymptotic analysis (perturbation theory), which is widely used in modern applied mathematics, mechanics and physics. But asymptotic methods ...