CRC Press eBooks

The Hydrogen-Like Atom

Ahmad Amer

Published Nov 5, 2025• 0 citations

Abstract

This chapter presents a detailed analysis of the hydrogen-like atom within the framework of quantum mechanics. The radial Schrödinger equation is solved for the Coulomb potential, yielding the quantized energy spectrum, energy eigenstates, and the associated degeneracy of levels. The expectation value of the electron's radius is calculated, and a comparison is drawn between quantum predictions and classical circular orbits. The quantum two-body problem is introduced to account for the motion of the nucleus, revealing its influence on the energy levels of the electron. This correction underpins the operation of the mass spectrometer and supports the spectroscopic identification of hydrogen isotopes such as deuterium and tritium. The analysis also explains how similar effects confirm the presence of helium in the solar spectrum through astrophysical observations. Metadata/Keywords: hydrogen-like atom, Coulomb potential, energy spectrum, quantum orbits, nucleus motion, two-body problem, mass spectrometer, hydrogen isotopes, helium, solar spectrum

DOI: 10.1201/9781003677109-7

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