In electrostatics, this equation reduces to Laplace’s equation if charge density is zero. For 10 points each:
[10h] Name this ubiquitous equation that, given a function f, is satisfied by a function whose Laplacian equals f.
ANSWER: Poisson’s equation [or Poisson equation]
[10m] For systems with this property, the Klein–Gordon equation reduces to a screened Poisson equation because the d’Alembertian reduces to the Laplacian. Autonomous systems have this property that names a form of the Schrödinger equation that can be written as “H Psi equals E Psi.”
ANSWER: time-independent [or time-invariant; accept descriptions of a system not being dependent on time; prompt on descriptions of a system not being dependent on its independent variable with “What is that independent variable?”] (In general, an autonomous system lacks explicit dependence on its independent variables. In physics, that independent variable is almost always time.)
[10e] Poisson’s equation for the Newtonian description of this weakest fundamental force includes a term for the Laplacian of the scalar potential of little g.
ANSWER: gravity [or gravitational force]
<Lalit Maharjan, Science - Physics> ~20453~ <Editor: David Bass>