A "clamped nuclear" one is employed by the Born-Oppenheimer approximation. Liouville's theorem demonstrates that it is the Noether charge corresponding to time translation invariance, and in quantum mechanics, it is a Hermitian, and therefore its eigenvectors generate a basis for its Hilbert space. Any smooth real-valued function on a symplectic space defines one, leading to an alternate derivation of the system that uses it, which often employs the Poisson bracket. FTP, identify this quantity, namesake of a reformulation of classical mechanics
A "clamped nuclear" one is employed by the Born-Oppenheimer approximation. Liouville's theorem demonstrates that it is the Noether charge corresponding to time translation invariance, and in quantum mechanics, it is a Hermitian, and therefore its eigenvectors generate a basis for its Hilbert space. Any smooth real-valued function on a symplectic space defines one, leading to an alternate derivation of the system that uses it, which often employs the Poisson bracket. FTP, identify this quantity, namesake of a reformulation of classical mechanics, which represents a system's total energy and is the Legendre transform of the Lagrangian.
A "clamped nuclear" one is employed by the Born-Oppenheimer approximation.
{Hamiltonian} mechanics