WeylAlgebra

WeylAlgebra[{vars, dvars}]
WeylAlgebra[{vars, dvars}, alg]

constructs a NonCommutativeAlgebra representing the Weyl algebra with variables vars and corresponding derivative generators dvars.

Example

alg = WeylAlgebra[{{x, y}, {dx, dy}}];
NonCommutativeExpand[dy ** dx ** x ** y, alg]

The second form takes operation names and monomial-order settings from alg.

See the official Wolfram Language reference for the defining commutation relations.