pith. sign in

arxiv: quant-ph/0006012 · v1 · submitted 2000-06-02 · 🪐 quant-ph

Classical trajectories compatible with quantum mechanics

classification 🪐 quant-ph
keywords particletrajectoryclassicalcannotconstantcorrespondinghowevermomentum
0
0 comments X
read the original abstract

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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.