Formally speaking, for a manifold Q, this makes use of the cotangent bundle T*Q
Formally speaking, for a manifold Q, this makes use of the cotangent bundle T*Q (T-star Q) instead of the tangent bundle TQ. It is more useful because it can directly provide first-order equations for both of the variables on T*Q, namely the position q and the canonical momentum p. It can be obtained from the Lagrangian L by the formula pq – L. FTP, what is this function which, in quantum mechanics, becomes the operator corresponding to energy?
Formally speaking, for a manifold Q, this makes use of the cotangent bundle T*Q
{Hamiltonian}