Quantum Free Particle and Internal Force

  In a previous note (1) we argued that a quantum free particle, represented by exp(ipx), carries the information of the force that created it and which it may also impart when striking a target  in the distributions cos(px), sin(px) of its wavefunction exp(ipx). In this note, we try to quantify this argument by first examining a second collective force in a quantum bound state other than -dV(x)/dx, namely KE(x) (-dW/dx / W) where W is the wavefunction. We argue this force should be present in a particle in a box with infinite walls and ultimately in a quantum free particle.Thus -id//dx, related to the translational operator, is linked to momentum and its conservation, but also ultimately to impulse carried by such a momentum, namely p. The force is found from pp/2m p where pp/2m is the frequency. Thus p is enough information for both momentum and force.. A high resolution (i.e. small wavelength) of a high momentum particle  is directly linked to the high force it may impart when striking a target. Alternatively, the notion that an impulse Integral F dt occurs at a  point x, as in two-body scattering in a Maxwell-Boltzmann gas, is only achieved in the high p limit, but an MB case is considered to be a high energy, high p limit i.e. a classical situation.