Question

The quantum mechanical operator for the momentum of a particle moving in one dimension is given by

Answer 1

(kinetic energy in one dimension) ... the quantum mechanical operators corresponding to the classical ... linear momentum along x, one of the postulates of quantum ...

Answer 2

The Hamiltonian operator, H, is the total energy operator, and it is made up of the kinetic and potential energy operators.

Because the derivative is a linear operator, the momentum operator is also linear, and also because the certain wave function can be expressed as a superposition of other states, the momentum eigenvalues for each plane wave component are obtained when this momentum operator is applied to the entire superimposed wave.

There is a quantum mechanical operator for each and every measurable property of a system. The Correspondence Principle is a term used to describe this.