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Psi function can refer, in mathematics, to the ordinal collapsing function ...
Greek letters are used in mathematics, science, engineering, and other areas where mathematical notation is used as symbols for constants, special functions, and also conventionally for variables representing certain quantities. In these contexts, the capital letters and the small letters represent distinct and unrelated entities.
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:
For n = 0, the equations reduce to the coupled Dirac equations and A and B together transform as the original Dirac spinor. Eliminating either A or B shows that A and B each fulfill . [2] The direct derivation of the Dirac-Pauli-Fierz equations using the Bargmann-Wigner operators is given in. [6]
In quantum field theory, if Φ out describes a state in the "distant future" (an "out state") after interactions between scattering particles have ceased, and Ψ in an "in state" in the "distant past", then the quantities (Φ out, Ψ in), with Φ out and Ψ in varying over a complete set of in states and out states respectively, is called the S ...
In thermodynamics, the Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol Ψ , is defined by the following relation:
The velocity satisfies the continuity equation for incompressible flow: ∇ ⋅ u = 0. {\displaystyle \quad \nabla \cdot \mathbf {u} =0.} Although in principle the stream function doesn't require the use of a particular coordinate system, for convenience the description presented here uses a right-handed Cartesian coordinate system with ...
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.