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Defining equation SI unit Dimension Wavefunction: ψ, Ψ To solve from the Schrödinger equation: varies with situation and number of particles Wavefunction probability density: ρ = | | = m −3 [L] −3: Wavefunction probability current: j: Non-relativistic, no external field:
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
The variational Mermin principle leads to an equation for the equilibrium density and system properties are calculated from the solution for the density. The equation is a non-linear integro-differential equation and finding a solution is not trivial, requiring numerical methods, except for the simplest models.
The convection–diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. For information about the equation, its derivation, and its conceptual importance and consequences, see the main article convection–diffusion equation. This article ...
The term Friedmann equation sometimes is used only for the first equation. [3] In these equations, R(t) is the cosmological scale factor, is the Newtonian constant of gravitation, Λ is the cosmological constant with dimension length −2, ρ is the energy density and p is the isotropic pressure.
Solving the equation by separation of variables means seeking a solution of the form of a product of spatial and temporal parts [19] (,) = (), where () is a function of all the spatial coordinate(s) of the particle(s) constituting the system only, and () is a function of time only.
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 equation is a nonlinear integro-differential equation, and the unknown function in the equation is a probability density function in six-dimensional space of a particle position and momentum. The problem of existence and uniqueness of solutions is still not fully resolved, but some recent results are quite promising. [3] [4]