In classical mechanics momentum is the derivative of position with respect to time. In quantum mechanics momentum is the gradient, i.e. the combination of the p

In classical mechanics momentum is the derivative of position with respect to time. In quantum mechanics momentum is the gradient, i.e. the combination of the partial derivatives with respect to the three directions of space, of the wave function [1], i.e. the probability amplitude of the particle as a function of position. In consequence, classically one can prepare a particle with any position and any momentum independently, i.e. one fixes the position and the time derivative of the position. Quantum mechanically fixing the position distribution also fixes the momentum distribution as the later is the derivative of the former with respect to space and therefore can not be specified independently. Similarly to the classical case one can also fix the time derivative of the wave function but that corresponds to the energy, not the momentum. [1] In position space.