The state-independent form of this equation can be solved with the assistance of a Hopf-Lax typeformula. This equation was extended as a continuous analog of the discrete deterministic dynamicprogramming equation by Richard Bellman. If a complex wavefunction is written as A times e to thequantity i S over h-bar, substituted into the Schrodinger equation, and h-bar is sent to zero, one finds thiseq
The state-independent form of this equation can be solved with the assistance of a Hopf-Lax typeformula. This equation was extended as a continuous analog of the discrete deterministic dynamicprogramming equation by Richard Bellman. If a complex wavefunction is written as A times e to thequantity i S over h-bar, substituted into the Schrodinger equation, and h-bar is sent to zero, one finds thisequation. This is the equation a generating function has to satisfy in order for it to be a canonicaltransformation. Two of the characteristic equations associated with it arise in the calculus of variations. Itautomatically yields all the constants of motion. For 10 points, identify this first-order nonlinear partialdifferential equation named for an English and German physicist, the former of whom also names aformulation of classical mechanics.
The state-independent form of this equation can be solved with the assistance of a Hopf-Lax typeformula.
Hamilton-Jacobi equation [or HJE; prompt on eikonal equation]