Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue

Ciann Dong Yang, Shiang Yi Han

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


The correspondence principle states that the quantum system will approach the classical system in high quantum numbers. Indeed, the average of the quantum probability density distribution reflects a classical-like distribution. However, the probability of finding a particle at the node of the wave function is zero. This condition is recognized as the nodal issue. In this paper, we propose a solution for this issue by means of complex quantum random trajectories, which are obtained by solving the stochastic differential equation derived from the optimal guidance law. It turns out that point set A, which is formed by the intersections of complex random trajectories with the real axis, can represent the quantum mechanical compatible distribution of the quantum harmonic oscillator system. Meanwhile, the projections of complex quantum random trajectories on the real axis form point set B that gives a spatial distribution without the appearance of nodes, and approaches the classical compatible distribution in high quantum numbers. Furthermore, the statistical distribution of point set B is verified by the solution of the Fokker–Planck equation.

Original languageEnglish
Pages (from-to)960-976
Number of pages17
JournalFoundations of Physics
Issue number9
Publication statusPublished - 2020 Sept 1

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


Dive into the research topics of 'Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue'. Together they form a unique fingerprint.

Cite this