A model of the hydrogen atom for l = 1 and l = 3 using the causal interpretation.
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Date
2025
Authors
Chiboli, Monica
Journal Title
Journal ISSN
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Publisher
The University of Zambia
Abstract
This study presents a model of the hydrogen atom for the orbital angular momentum l = 1 and l = 3 using the causal interpretation also referred to as the Bohm-de Broglie interpretation of quantum mechanics. The causal interpretation is an alternative interpretation of quantum mechanics that gives a description of underlying physical reality in terms of a single well-defined model which Bohr’s principle of complementarity claims to be impossible. This study presents detailed analytical calculations to determine the electron trajectories for the hydrogen atom states ψ21m and ψ43m. Further analytical calculations were made to determine the net force and magnitude of the angular momentum. The model was also extended to determine the trajectory of the rotated wave function. This was done both analytically and numerically using Maple. Maple was also used to plot the trajectories, net force, and angular momentum. The obtained results show that electrons have definite circular paths which are a result of the net force which is always directed to the z-axis. The results for the angular momentum show consistency with quantum mechanics, as the plots show that the angular momentum vector at various positions of the electron for a given value of m form a cone shape in its movement. The results also show that the electron is stationary form = 0, but rotates anti-clockwise for positive values of m and clockwise for negative values of m. From this work, it can be seen that the causal interpretation can be used to make models of quantum experiments/processes. This research therefore brings new light to the behaviour of an electron in atomic systems, thereby making contributions on the effort to develop a physical reality of quantum systems with implications in quantum chemistry and quantum physics. The presentation of this model also shows the effectiveness of Maple in developing computer models, especially in science and mathematics. Keywords: Causal interpretation, trajectories, wave function, Maple, hydrogen atom, net force, angular momentum.
Description
Thesis of Master of Science in Physics.