What does the quantum mechanics model of a hydrogen atom describe?


The quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical Coulomb potential.

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An electric field is generated by electrically charged particles and time-varying magnetic fields. The electric field describes the electric force experienced by a motionless positively electrically charged test particle at any point in space relative to the source(s) of the field. The concept of an electric field was introduced by Michael Faraday.

Coulomb's law or Coulomb's inverse-square law is a law of Chemistry describing the electrostatic interaction between electrically charged particles.

This law was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Newton's inverse-square law of universal gravitation. Coulomb's law can be used to derive Gauss's law, and vice versa.

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Quantum mechanics (QM – also known as quantum physics, or quantum theory) is a branch of physics which deals with physical phenomena at microscopic scales, where the action is on the order of the Planck constant. It departs from classical mechanics primarily at the quantum realm of atomic and subatomic length scales. Quantum mechanics provides a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It is the non-relativistic limit of Quantum Field Theory (QFT), a theory that was developed later that combined Quantum Mechanics with Relativity.

In advanced topics of quantum mechanics, some of these behaviors are macroscopic (see macroscopic quantum phenomena) and emerge at only extreme (i.e., very low or very high) energies or temperatures (such as in the use of superconducting magnets). The name quantum mechanics derives from the observation that some physical quantities can change only in discrete amounts (Latin quanta), and not in a continuous (cf. analog) way. For example, the angular momentum of an electron bound to an atom or molecule is quantized. In the context of quantum mechanics, the wave–particle duality of energy and matter and the uncertainty principle provide a unified view of the behavior of photons, electrons, and other atomic-scale objects.

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. This includes ions as well as neutral atoms and, unless otherwise stated, for the purposes of this discussion it should be assumed that the term atom includes ions.

The term atomic physics is often associated with nuclear power and nuclear bombs, due to the synonymous use of atomic and nuclear in standard English. However, physicists distinguish between atomic physics — which deals with the atom as a system consisting of a nucleus and electrons — and nuclear physics, which considers atomic nuclei alone.

The following outline is provided as an overview of and topical guide to physics:

Physics – natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.

A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the elemental mass of the universe. (Most of the universe's mass is not in the form of chemical elements—that is, "baryonic" matter—but is made up of dark matter and dark energy.)

In everyday life on Earth, isolated hydrogen atoms (usually called "atomic hydrogen" or, more precisely, "monatomic hydrogen") are extremely rare. Instead, hydrogen tends to combine with other atoms in compounds, or with itself to form ordinary (diatomic) hydrogen gas, H2. "Atomic hydrogen" and "hydrogen atom" in ordinary English use have overlapping, yet distinct, meanings. For example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen (which would refer to isolated hydrogen atoms).

Quantum mechanics is the body of scientific principles that explains the behaviour of matter and its interactions with energy on the scale of atoms and subatomic particles, and how these phenomena could be related to everyday life (see: Schrödinger's cat).

Classical physics explains matter and energy at the macroscopic level—on a scale familiar to human experience—including the behaviour of astronomical bodies. It remains the key to measurement for much of modern science and technology. On the other hand, toward the end of the 19th century, scientists discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain. Coming to terms with these limitations led to the development of quantum mechanics, a major revolution in physics. This article describes how physicists discovered the limitations of classical physics and developed the main concepts of the quantum theory that replaced it in the early decades of the 20th century. These concepts are described in roughly the order they were first discovered; for a more complete history of the subject, see History of quantum mechanics.


A Rydberg atom is an with one or more electrons that have a very high principal quantum number. These atoms have a number of peculiar properties including an exaggerated response to electric and magnetic fields, long decay periods and electron wavefunctions that approximate, under some conditions, classical orbits of electrons about the nuclei. The core electrons shield the outer electron from the electric field of the nucleus such that, from a distance, the electric potential looks identical to that experienced by the electron in a hydrogen atom.

In spite of its shortcomings, the Bohr model of the atom is useful in explaining these properties. Classically an electron in a circular orbit of radius r, about a hydrogen nucleus of charge +e, obeys Newton's second law:

Tunnel ionization is a process in which electrons in an atom (or a molecule) pass through the potential barrier and escape from the atom (or molecule). In an intense electric field, the potential barrier of an atom (molecule) is distorted drastically. Therefore, the length of the barrier that electrons have to pass decreases and electrons can escape from the atom (molecule) easily. Tunneling Ionization is a QM phenomenon; a non-zero probability event for observing a particle escaping from the deformed Coulomb potential barrier, obviously this phenomenon is forbidden by classical laws, as in the classical picture an electron does not have sufficient energy to escape.

When the atom is in an external DC field, the Coulomb potential barrier is lowered and the electron can tunnel through the barrier. In the case of an alternating electric field, the direction of the electric field reverses after the half period of the field. The ionized electron may come back to its parent ion. The electron may recombine with the nucleus (nuclei) and its kinetic energy is released as light (high harmonic generation). If the recombination does not occur, further ionization may proceed by collision between high-energy electrons and a parent atom (molecule). This process is known as non-sequential ionization.

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