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  2. Energy–momentum relation - Wikipedia

    en.wikipedia.org/wiki/Energy–momentum_relation

    In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.

  3. List of relativistic equations - Wikipedia

    en.wikipedia.org/wiki/List_of_relativistic_equations

    This is the formula for the relativistic doppler shift where the difference in velocity between the emitter and observer is not on the x-axis. There are two special cases of this equation. The first is the case where the velocity between the emitter and observer is along the x-axis. In that case θ = 0, and cos θ = 1, which gives:

  4. Bohr–Sommerfeld model - Wikipedia

    en.wikipedia.org/wiki/Bohr–Sommerfeld_model

    Arnold Sommerfeld derived the relativistic solution of atomic energy levels. [5] We will start this derivation [ 10 ] with the relativistic equation for energy in the electric potential W = m 0 c 2 ( 1 1 − v 2 c 2 − 1 ) − k Z e 2 r {\displaystyle W={m_{\mathrm {0} }c^{2}}\left({\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}-1\right)-k{\frac ...

  5. Klein–Gordon equation - Wikipedia

    en.wikipedia.org/wiki/Klein–Gordon_equation

    Any solution of the free Dirac equation is, for each of its four components, a solution of the free Klein–Gordon equation. Despite historically it was invented as a single particle equation the Klein–Gordon equation cannot form the basis of a consistent quantum relativistic one-particle theory, any relativistic theory implies creation and ...

  6. Mass in special relativity - Wikipedia

    en.wikipedia.org/wiki/Mass_in_special_relativity

    The equation is often written this way because the difference is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems. Where m > 0 and p = 0, this equation again expresses the mass–energy equivalence E = m.

  7. Relativistic mechanics - Wikipedia

    en.wikipedia.org/wiki/Relativistic_mechanics

    The relativistic four-velocity, that is the four-vector representing velocity in relativity, is defined as follows: = = (,) In the above, is the proper time of the path through spacetime, called the world-line, followed by the object velocity the above represents, and

  8. Dirac equation - Wikipedia

    en.wikipedia.org/wiki/Dirac_equation

    The left side represents the square of the momentum operator divided by twice the mass, which is the non-relativistic kinetic energy. Because relativity treats space and time as a whole, a relativistic generalization of this equation requires that space and time derivatives must enter symmetrically as they do in the Maxwell equations that ...

  9. Relativistic Euler equations - Wikipedia

    en.wikipedia.org/wiki/Relativistic_Euler_equations

    The equations of motion are contained in the continuity equation of the stress–energy tensor: =, where is the covariant derivative. [5] For a perfect fluid, = (+) +. Here is the total mass-energy density (including both rest mass and internal energy density) of the fluid, is the fluid pressure, is the four-velocity of the fluid, and is the metric tensor. [2]