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  2. Bifurcation theory - Wikipedia

    en.wikipedia.org/wiki/Bifurcation_theory

    Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.

  3. Heisenberg picture - Wikipedia

    en.wikipedia.org/wiki/Heisenberg_picture

    In physics, the Heisenberg picture or Heisenberg representation [1] is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which observables incorporate a dependency on time, but the states are time-independent.

  4. Multiple integral - Wikipedia

    en.wikipedia.org/wiki/Multiple_integral

    Example of a domain transformation from cartesian to polar. Example 2c. The domain is D = {x 2 + y 2 ≤ 4}, that is a circumference of radius 2; it's evident that the covered angle is the circle angle, so φ varies from 0 to 2 π, while the crown radius varies from 0 to 2 (the crown with the inside radius null is just a circle). Example 2d.

  5. Perturbation theory - Wikipedia

    en.wikipedia.org/wiki/Perturbation_theory

    Perturbation theory has been used in a large number of different settings in physics and applied mathematics. Examples of the "collection of equations" include algebraic equations, [6] differential equations [7] (e.g., the equations of motion [8] and commonly wave equations), thermodynamic free energy in statistical mechanics, radiative ...

  6. List of equations in quantum mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in...

    One particle: N particles: One dimension ^ = ^ + = + ^ = = ^ + (,,) = = + (,,) where the position of particle n is x n. = + = = +. (,) = /.There is a further restriction — the solution must not grow at infinity, so that it has either a finite L 2-norm (if it is a bound state) or a slowly diverging norm (if it is part of a continuum): [1] ‖ ‖ = | |.

  7. Reaction–diffusion system - Wikipedia

    en.wikipedia.org/wiki/Reaction–diffusion_system

    The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space. Reaction–diffusion systems are naturally applied in chemistry. However, the ...

  8. Do pedestrians have to clear the road before you enter the ...

    www.aol.com/news/pedestrians-clear-road-drive...

    One example of when officers will cite a motorist for not properly yielding to a pedestrian in a ... This means pedestrians legally have the right of way even when not using a marked crosswalk.

  9. Generating function (physics) - Wikipedia

    en.wikipedia.org/wiki/Generating_function_(physics)

    Common examples are the partition function of statistical mechanics, the Hamiltonian, and the function which acts as a bridge between two sets of canonical variables when performing a canonical transformation.