EMG. Voluntary. reaction. Perturbation. M 2. M 3. M 1. Time. Lecture 12: Pre-Programmed Reactions.

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Perturbation. Simple system with added effect. Basic Lagrangian L 0 Perturbing term U Express as a perturbed Hamiltonian. Formed in the usual way Write as a first-order power series. l = 1 for perturbed motion. Perturbed System. Time-independent systems can use J, w .

. Perturbation Theory. Perturbation Theory. For Keplerian motion all elements are constant in time (except M that changes linearly)For arbitrary motion one can think in the time changing orbital elements as a transformation of coordinates.Osculating orbit

Perturbation: Background. Algebraic Differential Equations. Perturbed equation. Original Equation. Perturbation. Perturbed equation. Answer can be in the form. Perturbation. Change in result (absolute values) vs Change in equation. Simple (Regular) Perturbation. Perturbed equation.

Perturbation theory. We begin with an unperturbed Hamiltonian H0 , which is also assumed to have no time dependence. It has known energy levels and eigenstates, arising from the time-independent Schrödinger equation :

Perturbation Theory. March 11, 2013. Just So You Know. The Fourier Analysis/Vocal Tract exercise is due on Wednesday. Please note: don’t make too much out of rounding off errors!. With a neutral vowel, we’re somewhere in the middle of the acoustic vowel space.

SYMBOLIC PERTURBATION. The problem. Algorithms in computational geometry make certain assumptions about the input (general status). The treatment of cases violating these assumptions (degeneracies) is tedious, and seldom included in the theoretical discussion.

Perturbation Theory. H 0 is the Hamiltonian of for a known system for which we have the solutions: the energies, e 0 , and the wavefunctions, f 0 . H 0 f 0 = e 0 f 0

Perturbation Theory . Only a few QM systems that can be solved exactly: Hydrogen Atom(simplified), harmonic oscillator, infinite+finite well solve using perturbation theory which starts from a known solution and makes successive approx- imations (derived slightly differently in Griffiths)

Perturbation Theory . Only a few QM systems that can be solved exactly: Hydrogen Atom(simplified), harmonic oscillator, infinite+finite well solve using perturbation theory which starts from a known solution and makes successive approx- imations start with time independent. V’(x)=V(x)+v(x)

PERTURBATION THEORY. Time Independent Theory. A Necessity:. Exactly solvable problems are very few and do not really represent a real physical system completely. In many cases, the primary interaction on the system maybe exactly solvable and is hence the dominant contribution.