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  2. List of relativistic equations - Wikipedia

    en.wikipedia.org/wiki/List_of_relativistic_equations

    To derive the equations of special relativity, one must start with two other The laws of physics are invariant under transformations between inertial frames. In other words, the laws of physics will be the same whether you are testing them in a frame 'at rest', or a frame moving with a constant velocity relative to the 'rest' frame.

  3. List of equations in quantum mechanics - Wikipedia

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

    To solve from the Schrödinger equation: ... Position-momentum Fourier transform (1 particle in 3d) ... List of equations in nuclear and particle physics; List of ...

  4. Mathematical formulation of the Standard Model - Wikipedia

    en.wikipedia.org/wiki/Mathematical_formulation...

    In particular, under weak isospin SU(2) transformations the left-handed particles are weak-isospin doublets, whereas the right-handed are singlets – i.e. the weak isospin of ψ R is zero. Put more simply, the weak interaction could rotate e.g. a left-handed electron into a left-handed neutrino (with emission of a W − ), but could not do so ...

  5. Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fourier_transform

    By applying the Fourier transform and using these formulas, some ordinary differential equations can be transformed into algebraic equations, which are much easier to solve. These formulas also give rise to the rule of thumb "f(x) is smooth if and only if f̂(ξ) quickly falls to 0 for | ξ | → ∞."

  6. Symplectic integrator - Wikipedia

    en.wikipedia.org/wiki/Symplectic_integrator

    Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in nonlinear dynamics, molecular dynamics, discrete element methods, accelerator physics, plasma physics, quantum physics, and celestial mechanics.

  7. Canonical transformation - Wikipedia

    en.wikipedia.org/wiki/Canonical_transformation

    Restricted canonical transformations are coordinate transformations where transformed coordinates Q and P do not have explicit time dependence, i.e., = (,) and = (,).The functional form of Hamilton's equations is ˙ =, ˙ = In general, a transformation (q, p) → (Q, P) does not preserve the form of Hamilton's equations but in the absence of time dependence in transformation, some ...

  8. Derivations of the Lorentz transformations - Wikipedia

    en.wikipedia.org/wiki/Derivations_of_the_Lorentz...

    In the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and tensors containing physical quantities transform from one frame of reference to another.

  9. Spectral method - Wikipedia

    en.wikipedia.org/wiki/Spectral_method

    Compute the Fourier transform (b j,k) of g.Compute the Fourier transform (a j,k) of f via the formula ().Compute f by taking an inverse Fourier transform of (a j,k).; Since we're only interested in a finite window of frequencies (of size n, say) this can be done using a fast Fourier transform algorithm.