Generalizations
The simple formula
valid for the quantization of the simplest classical system, can be generalized to the case of an arbitrary Lagrangian . We identify canonical coordinates (such as x in the example above, or a field φ(x) in the case of quantum field theory) and canonical momenta πx (in the example above it is p, or more generally, some functions involving the derivatives of the canonical coordinates with respect to time):
This definition of the canonical momentum ensures that one of the Euler–Lagrange equations has the form
The canonical commutation relations then amount to
where δij is the Kronecker delta.
Further, it can be easily shown that
Read more about this topic: Canonical Commutation Relation