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Classical trajectories compatible with quantum mechanics | | B. Roy Frieden
; A. Plastino
; | | Date: |
2 Jun 2000 | | Subject: | quant-ph | | 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. | | Source: | arXiv, quant-ph/0006012 | | Services: | Forum | Review | PDF | Favorites | |
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