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change in a variable (e.g. ) unitless Laplace operator: per square meter (m −2) displacement (usually small) meter (m) Dirac delta function: Kronecker delta (e.g ) epsilon: permittivity: farad per meter (F/m) strain: unitless
Canonical commutation rule for position q and momentum p variables of a particle, 1927.pq − qp = h/(2πi).Uncertainty principle of Heisenberg, 1927. The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics.
In electronic/electrical circuits, the voltages of the nodes and the currents through components in the circuit are usually the state variables. In any electrical circuit, the number of state variables are equal to the number of (independent) storage elements, which are inductors and capacitors. The state variable for an inductor is the current ...
The Hamiltonian is defined by = = ˙ ˙ and can be obtained by performing a Legendre transformation on the Lagrangian, which introduces new variables canonically conjugate to the original variables. For example, given a set of generalized coordinates, the variables canonically conjugate are the generalized momenta. This doubles the number of ...
A differential equation of motion, usually identified as some physical law (for example, F = ma), and applying definitions of physical quantities, is used to set up an equation to solve a kinematics problem. Solving the differential equation will lead to a general solution with arbitrary constants, the arbitrariness corresponding to a set of ...
Gather all the independent variables that are likely to influence the dependent variable. If R is a variable that depends upon independent variables R 1, R 2, R 3, ..., R n, then the functional equation can be written as R = F(R 1, R 2, R 3, ..., R n). Write the above equation in the form R = C R 1 a R 2 b R 3 c...
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties.This is often written as = or =, where = = is the Laplace operator, [note 1] is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and (,,) is a twice-differentiable real-valued function.