Quantum Mechanics & Force: Wave-Particle Duality

[cam875]

if matter in QM is considered to be more like waves with that particle duality what happens when a force is applied in QM, is it like classical where the force is a vector or does that change also in QM.

 

[diegzumillo]

Someone correct me if I'm wrong :)

I think that in QM we rely on the concept of fields.

 

[vanesch]

Force is a concept in Newtonian mechanics that describes an interaction between two subsystems (say, two particles). In quantum theory, one has a different way to do so: one describes the interaction potential (which, in the case of the quantum description of a classical system, is indeed the potential energy that would give you the said force). The geometrical meaning of a force as a vector is lost in quantum mechanics (that is, you can't do anything with it, except use it to derive the interaction potential).

For instance, if you have two charged particles at positions p1 and p2, then you will have an interaction potential due to Coulomb's "force" as given by q1 q2 /(4 pi eps0 |p1 - p2|)

This term will enter into the Schroedinger equation which tells you how the quantum state (the "waves" if you want to) will change, and lo and behold, they will change in a way which resembles the action of a repulsive or attractive force.

 

[cam875]

alright thanks.

 

[malawi_glenn]

The reason why we don't speak of force is that QM is based on Hamiltonian mechanics, which is Kinetic + Potential Term.