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Rethinking the Boundary Conditions in the Particle-in-a-Box Mind Experiment

revised on 12.04.2021, 23:17 and posted on 13.04.2021, 07:51 by Jixin Chen

In this manuscript, I speculated that the energy density distributions along space and time in a quantum system are uniform. Thus, the complementary energy contributions are added to the classical solutions of the 1D particle in a box problem, making the energy density a complex distribution function over space and time. Then the concept is extended to the free rotation problem with a Hamiltonian slightly different than the classical Schrödinger equation. The picturized energy distribution functions and associated time evolution are described in movies for comparison between example classical wave functions and the energy density functions. The wave functions for the hydrogen atom are then guessed based on the historical solutions.


Email Address of Submitting Author


Ohio University


United States

ORCID For Submitting Author


Declaration of Conflict of Interest


Version Notes

3rd version