Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Royal Society of Chemistry eBooks

Atomic particles, photons and the quantization of electron energies; Heisenberg's uncertainty principle

Jack Barrett

Published Feb 28, 2002• 0 citations
Publisher
DOI
10.1039/9781847550187-00001

Related papers

Wave-Particle Duality

Reinhold A. Bertlmann, Nicolai Friis

Abstract This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat

•Sep 7, 2023•0 citations

THE QUANTUM LAWS AND THE UNCERTAINTY PRINCIPLE OF HEISENBERG

Gilbert Newton Lewis, Joseph E. Mayer

Proceedings of the National Academy of Sciences•Feb 15, 1929•12 citations

Operators, Oscillations, Uncertainty, and Quanta

Steven M. Pascal

Several somewhat independent concepts are introduced in this chapter. First, we've stated that the wave equation contains information about the particle. How is the information extracted? By using operators, which often include derivative operations. By "operating" on the wave function, we can pull out certain factors, such as the momentum or the energy of the particle. Here, three operators are discussed: the total energy operator in terms of a time-derivative; a more space-based energy operator called the Hamiltonian, which simply represents the kinetic energy plus the potential energy; and the momentum operator. Second, we show that an oscillating wave function does not necessarily mean that the particle position is oscillating, since the position is related to the square modulus of the wave function. Third, the Heisenberg uncertainty principle is introduced using a free particle with specified energy, but with no specified position. Fourth, the idea of "quantization" is introduced. The quantization, or the existence of only certain allowed energies, arises when the particle is not free but is trapped by a potential, such as an electron trapped in an atom. Since trapped particles are very important to scientists, the entire subject is called "quantum" science.

CRC Press eBooks•Jul 12, 2023•0 citations

The Uncertainty Principle of Heisenberg

John Stringer

Elsevier eBooks•Jan 1, 1967•0 citations

Reviving Bohr Molecules

Gilbert Chin

Before the Heisenberg-Schrödinger formulation of quantum mechanics, the semiclassical Bohr-Sommerfeld theory successfully accounted for quantized properties such as the energy levels in the hydrogen atom. However, the forcing of closed orbits for particle motion ran afoul of the uncertainty principle. Recently, the use of Dscaling, in which the motion of each particle is described by a vector in D dimensions, was used to reintroduce the uncertainty principle to this earlier theory. When properly done, such equations reduce to the correct Schrödinger form for D = 3 but can still be solved in the more tractable D→ ∞ limit. This D scaling approach was applied successfully to atoms but did not yield bound states for molecules.

Science•Sep 1, 2005•0 citations

Atoms, Photons, and Quantum Mechanics

Charles H. Holbrow, James N. Lloyd, Joseph C. Amato +2 more

Springer eBooks•Jan 1, 2009•0 citations
Abstract This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat
Several somewhat independent concepts are introduced in this chapter. First, we've stated that the wave equation contains information about the particle. How is the information extracted? By using operators, which often include derivative operations. By "operating" on the wave function, we can pull out certain factors, such as the momentum or the energy of the particle. Here, three operators are discussed: the total energy operator in terms of a time-derivative; a more space-based energy operator called the Hamiltonian, which simply represents the kinetic energy plus the potential energy; and the momentum operator. Second, we show that an oscillating wave function does not necessarily mean that the particle position is oscillating, since the position is related to the square modulus of the wave function. Third, the Heisenberg uncertainty principle is introduced using a free particle with specified energy, but with no specified position. Fourth, the idea of "quantization" is introduced. The quantization, or the existence of only certain allowed energies, arises when the particle is not free but is trapped by a potential, such as an electron trapped in an atom. Since trapped particles are very important to scientists, the entire subject is called "quantum" science.
Before the Heisenberg-Schrödinger formulation of quantum mechanics, the semiclassical Bohr-Sommerfeld theory successfully accounted for quantized properties such as the energy levels in the hydrogen atom. However, the forcing of closed orbits for particle motion ran afoul of the uncertainty principle. Recently, the use of Dscaling, in which the motion of each particle is described by a vector in D dimensions, was used to reintroduce the uncertainty principle to this earlier theory. When properly done, such equations reduce to the correct Schrödinger form for D = 3 but can still be solved in the more tractable D→ ∞ limit. This D scaling approach was applied successfully to atoms but did not yield bound states for molecules.