k r" all over "four pi r." This man's equation is de⎜ned as the Laplacian of a scalar or vector function, F, plus "k-squared times F" equals zero, and it reduces to Laplace's equation when k equals zero.
Morse and Feshbach determined the coordinate systems in which this man's equation is separable by imposing the Robertson condition on the Stackel determinant. In 3D, the Green's function for this man's equation is "minus e" to the "plus or minus i k r" all over "four pi r." This man's equation is de⎜ned as the Laplacian of a scalar or vector function, F, plus "k-squared times F" equals zero, and it reduces to Laplace's equation when k equals zero. By this man's theorem, any ⎜nite, uniform, continuous, vanishing vector ⎜eld can be expressed as the gradient of a scalar plus the curl of a vector with zero divergence. The useful work obtainable from a closed thermodynamic system is known as, for 10 points, what German scientist's namesake "free energy"?
Morse and Feshbach determined the coordinate systems in which this man's equation is separable by imposing the Robertson condition on the Stackel determinant.
Hermann von Helmholtz [or Hermann Ludwig Ferdinand Helmholtz; accept Helmholtz equation or Helmholtz theorem or Helmholtz free energy]