In special relativity, this scalar quantity is divided by the speed of light and grouped with momentum to form a four-vector.
Under a canonical transformation, the operator for this quantity is replaced by its old form plus the partial time derivative of the generating function. When separating variables in the Hamilton–Jacobi equation, this quantity multiplied by time gives the difference between Hamilton's characteristic and principal functions. The sign of this quantity determines whether an orbit has an eccentricity greater or less than 1, since it is negative only for bound orbits. A system with time translation symmetry will conserve this quantity according to Noether's ("NUR-tuh's") theorem. In special relativity, this scalar quantity is divided by the speed of light and grouped with momentum to form a four-vector. For 10 points, name this quantity calculated by the Hamiltonian operator, which has kinetic and potential components.
Under a canonical transformation, the operator for this quantity is replaced by its old form plus the partial time derivative of the generating function.
energy [accept total energy; do not accept or prompt on specific types such as “kinetic energy” or “potential energy”] &lt;Physics&gt;