Abstract
Some of the problems that were the center of discussions during the long genesis of the quantum theory were the atomic structure and the radiated spectral lines, in particular the emission lines of Hydrogen. A convincing explanation of this problem had to wait to the advent of the quantum theory. The Bohr postulates were, as will be seen below, unable to explain convincingly the electronic configuration and the spectral lines of atoms in the presence of a magnetic field. The application of the quantum theory to the atomic problem was undoubtedly the litmus test of the new theory.
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Notes
- 1.
If we do not make this assumption, the Hydrogen kinetic energy will be the sum of the proton and the electron kinetic energies. At the end of this chapter, in the solved problems section, we show that the two-particle problem can be reduced to that of two quasi-particles: the center of mass, with mass \(m+m_p\) (\(m\) is the mass of electron and \(m_p\) is the mass of proton), and the relative particle with mass \(\mu =mm_p/(m+m_p)\). As this mass differs by less than \(1\%\) from \(m\), the problem is essentially equivalent to assuming that the proton is at rest, and the electron orbits around it.
- 2.
The \(Z-1\) electrons of the inner levels have roughly a spherical distribution, their effect on the valence band electron is then negligible.
- 3.
These polynomials are also called associated Laguerre’s polynomials. In the literature of these polynomials there are variations in the notation and definition that should be taken into account.
- 4.
W. Pauli , Z. Physik 31, 765 (1925).
- 5.
Hendrik Antoon Lorentz and Pieter Zeeman shared the Nobel Prize in physics in 1902.
- 6.
This is known as the symmetric Coulomb gauge.
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© 2012 Springer-Verlag Berlin Heidelberg
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Pereyra Padilla, P. (2012). The Hydrogen Atom. In: Fundamentals of Quantum Physics. Undergraduate Lecture Notes in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29378-8_10
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DOI: https://doi.org/10.1007/978-3-642-29378-8_10
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