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To solve from the Schrödinger equation: ... List of equations in nuclear and particle physics; List of equations in wave theory; List of photonics equations;
Integral equation methods, however, generate dense (all entries are nonzero) linear systems, making such methods preferable to FD or FEM only for small problems. Such systems require O(n 2) memory to store and O(n 3) to solve via direct Gaussian elimination or, at best, O(n 2) if solved iteratively. Increasing circuit speeds and densities ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
The Maxwell–Bloch equations, also called the optical Bloch equations [1] describe the dynamics of a two-state quantum system interacting with the electromagnetic mode of an optical resonator. They are analogous to (but not at all equivalent to) the Bloch equations which describe the motion of the nuclear magnetic moment in an electromagnetic ...
In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space.
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0
In quantum field theory, a nonlinear σ model describes a field Σ that takes on values in a nonlinear manifold called the target manifold T.The non-linear σ-model was introduced by Gell-Mann & Lévy (1960, §6), who named it after a field corresponding to a spinless meson called σ in their model. [1]