Microscopic Aspects of Force in Quantum Mechanics

    In a previous note (1), it was shown that by taking the derivative of the time-independent Schrodinger equation in the form: -1/2m (d/dx d/dx W /W) + V(r)=E  yields an equation linking various fluxes to–d/dx V i.e. force. In other notes, it was shown the time-independent Schrodinger equation may be written microscopically for each p momentum plane wave as:

   p²/2m f(p) + Sum j+k=p  Vj f(k) = E f(p)   ((1))

Here, the same E (energy) applies to all p momentum  waves. Thus, it is as if there is a dynamical resonance for each p wave, with various k momentum waves combining with the potential (Vj= the jth Fourier transform of V(r)) to form a p momentum wave. In this note, we wish to examine force microscopically in terms of ((1)) and also to consider the effects of noninertial frames or constrained motion on microscopic force.