Classical trajectories compatible with quantum mechanics

Details Classical trajectories compatible with quantum mechanics Classical trajectories compatible with quantum mechanics

2000-06-02

arxiv.org/abs/quant-ph/0006012v1

Physics

Quantum Physics

Scientific paper

10.1016/S0375-9601(01)00481-9

Consider any stationary Schroedinger wave equation (SWE) solution $psi (x)$ for a particle. The corresponding PDF on position QTR{em}{x} of the particle is QTR{em}{p}$_{X}(x)=|psi (x)|^{2}$. There is a classical trajectory QTR{em}{x(t)} for the particle that is consistent with this PDF. The trajectory is unique to within an additive constant corresponding to an initial condition QTR{em}{x(0).} However the value of QTR{em}{x(0)} cannot be known. As an example, a free particle in its ground state in a box of length QTR{em}{L} obeys a classical trajectory QTR{em}{x/L - (1/2}$pi)sin (2pi x/L)+t_{0}=t.$ The constant QTR{em}{t}$_{0}$ is an unknowable time displacement. Momentum values, however, cannot be determined by merely differentiating QTR{em}{d/dt} the trajectory QTR{em}{x(t)} and, instead, follow the usual quantification rules of Heisenberg's. This permits position and momentum to remain complementary variables. Our approach is fundamentally different from that of D. Bohm.

Affiliated with

Also associated with

No associations

Rating

Classical trajectories compatible with quantum mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classical trajectories compatible with quantum mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical trajectories compatible with quantum mechanics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-410465