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Volume 12: Pages 332-339, 1999
Quantum Theory of the Free Particle
West Area, 37# Building, 1 Floor, 26#, Central China Normal University, Wuhan, Hubei PRO., People's Republic of China
In this paper, based on the uncertainty principle and the principle that the values of probability measured by different inertial frames are the same, we obtain directly the probability distribution density function of velocity and momentum for a nonrelativistic and relativistic point particle when the position of the particle is fully measured. We also obtain directly the position distribution function and three‐dimensional current density of a free particle. Among our conclusions, we note that the relativistic case differs from current quantum mechanics. In addition, we obtain three integration formulas using Dirac theory, and, based on these formulas, give a new calculation for the probability that the eigenvalue an is observed when physical quantity A is measured for a state described by the state vector | ψ .
Keywords: uncertainty principle, probability distribution density function, Dirac theory of the free particle
Received: October 20, 1998; Published online: December 15, 2008