TY - JOUR

T1 - Incompleteness of trajectory-based interpretations of quantum mechanics

AU - Hall, Michael J.W.

PY - 2004/10/8

Y1 - 2004/10/8

N2 - Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition of the Schrödinger equation into a continuity equation and a modified Hamilton-Jacobi equation, fails for some quantum states. A very simple example is provided by a quantum particle in a box, described by a wavefunction that is initially uniform over the interior of the box. For this example, there is no corresponding continuity or modified Hamilton-Jacobi equation, and the space-time dependence of the wavefunction has a known fractal structure. Examples with finite average energies are also constructed.

AB - Trajectory-based approaches to quantum mechanics include the de Broglie-Bohm interpretation and Nelson's stochastic interpretation. It is shown that the usual route to establishing the validity of such interpretations, via a decomposition of the Schrödinger equation into a continuity equation and a modified Hamilton-Jacobi equation, fails for some quantum states. A very simple example is provided by a quantum particle in a box, described by a wavefunction that is initially uniform over the interior of the box. For this example, there is no corresponding continuity or modified Hamilton-Jacobi equation, and the space-time dependence of the wavefunction has a known fractal structure. Examples with finite average energies are also constructed.

UR - http://www.scopus.com/inward/record.url?scp=6344240780&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/37/40/015

DO - 10.1088/0305-4470/37/40/015

M3 - Article

SN - 0305-4470

VL - 37

SP - 9549

EP - 9556

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 40

ER -