The body‐point model and its application to describe the motion of an electron near the nucleus of a hydrogen atom

• Published in: Zeitschrift für angewandte Mathematik und Mechanik 2023-10, Vol.103 (10), p.n/a
• Main Authors: Ivanova, Elena A., Tur, Vsevolod D.
• Format: Article
• Language: English
• Subjects: Hydrogen atoms; Moments of inertia; Potential fields; Rigid structures; Trajectories
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.202200355

We consider the motion of a body‐point near an attracting center. The body‐point is defined as a particle with the following properties. (a) The body‐point occupies zero volume in space like a point mass. (b) The body‐point has both translational and rotational degrees of freedom like a rigid body. (c) The body‐point is characterized by a larger number of moments of inertia than an ordinary rigid body. Due to the additional moments of inertia, the body‐point acquires dynamic properties that are fundamentally different from the dynamic properties of an ordinary rigid body. We show that the trajectory of the body‐point moving near the attracting center is a spatial curve, and not a flat one, as it would be in the case of a point mass or a rigid body. We study in detail a special case of the body‐point motion, in which the magnitude of the momentum vector remains constant. We show that, in this special case, the region of space where the trajectory of the body‐point is located can be interpreted as the orbital of an electron in a hydrogen atom. Assuming that the body‐point models the electron in the ground energy state, we determine the parameters of our model. We emphasize that the problem of the body‐point motion near an attracting center is considered for the first time, and therefore all theoretical results presented in this paper are novel. Also, for the first time, the model of the body‐point in a central potential field is used to describe the behavior of an electron in a hydrogen atom. We consider the motion of a body‐point near an attracting center. The body‐point is defined as a particle with the following properties. (a) The body‐point occupies zero volume in space like a point mass. (b) The body‐point has both translational and rotational degrees of freedom like a rigid body. (c) The body‐point is characterized by a larger number of moments of inertia than an ordinary rigid body. Due to the additional moments of inertia, the body‐point acquires dynamic properties that are fundamentally different from the dynamic properties of an ordinary rigid body.