quantum number

(noun)

One of certain integers or half-integers that specify the state of a quantum mechanical system (such as an electron in an atom).

Related Terms

Examples of quantum number in the following topics:

  • Quantum Numbers

    • Quantum numbers provide a numerical description of the orbitals in which electrons reside.
    • The first quantum number describes the electron shell, or energy level, of an atom.
    • The second quantum number, known as the angular or orbital quantum number, describes the subshell and gives the magnitude of the orbital angular momentum through the relation.
    • The value of the mℓ quantum number is associated with the orbital orientation.
    • For example, the quantum numbers of electrons from a magnesium atom are listed below.

  • Wave Equation for the Hydrogen Atom

    • The angular momentum quantum number ℓ = 0, 1, 2, ... determines the magnitude of the angular momentum.
    • This leads to a third quantum number, the principal quantum number n = 1, 2, 3, ....
    • The principal quantum number in hydrogen is related to the atom's total energy.
    • Note that the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i.e. ℓ = 0, 1, ..., n − 1.
    • Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers.

  • Description of the Hydrogen Atom

    • Therefore, the energy eigenstates may be classified by two angular momentum quantum numbers, ℓ and m (both are integers).
    • The angular momentum quantum number ℓ = 0, 1, 2, ... determines the magnitude of the angular momentum.
    • This leads to a third quantum number, the principal quantum number n = 1, 2, 3, ....
    • The principal quantum number in hydrogen is related to the atom's total energy.
    • Note the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1, i.e. ℓ = 0, 1, ..., n − 1.

  • Implications of Quantum Mechanics

    • Quantum mechanics has also strongly influenced string theory.
    • The application of quantum mechanics to chemistry is known as quantum chemistry.
    • A great number of modern technological inventions operate on a scale where quantum effects are significant.
    • Another topic of active research is quantum teleportation, which deals with techniques to transmit quantum information over arbitrary distances.
    • Explain importance of quantum mechanics for technology and other branches of science

  • Quantum-Mechanical View of Atoms

    • Hydrogen-1 (one proton + one electron) is the simplest form of atoms, and not surprisingly, our quantum mechanical understanding of atoms evolved with the understanding of this species.
    • Modern quantum mechanical view of hydrogen has evolved further after Schrödinger, by taking relativistic correction terms into account.
    • Quantum electrodynamics (QED), a relativistic quantum field theory describing the interaction of electrically charged particles, has successfully predicted minuscule corrections in energy levels.
    • One of the hydrogen's atomic transitions (n=2 to n=1, n: principal quantum number) has been measured to an extraordinary precision of 1 part in a hundred trillion.
    • This kind of spectroscopic precision allows physicists to refine quantum theories of atoms, by accounting for minuscule discrepancies between experimental results and theories.

  • Indeterminacy and Probability Distribution Maps

    • An adequate account of quantum indeterminacy requires a theory of measurement.
    • Many theories have been proposed since the beginning of quantum mechanics, and quantum measurement continues to be an active research area in both theoretical and experimental physics.
    • In quantum mechanical formalism, it is impossible that, for a given quantum state, each one of these measurable properties (observables) has a determinate (sharp) value.
    • In the world of quantum phenomena, this is not the case.
    • As indicated by the quantum numbers (n, l, ml), this figure depicts probability clouds for the electron in the ground state and several excited states of hydrogen.

  • Photochemistry

    • This "photoequivalence law" was derived by Albert Einstein during his development of the quantum (photon) theory of light.
    • The efficiency with which a given photochemical process occurs is given by its Quantum Yield (Φ).
    • Since many photochemical reactions are complex, and may compete with unproductive energy loss, the quantum yield is usually specified for a particular event.
    • Thus, we may define quantum yield as "the number of moles of a stated reactant disappearing, or the number of moles of a stated product produced, per einstein of monochromatic light absorbed
    • Several secondary radical reactions then follow (shown in the gray box), making it difficult to assign a quantum yield to the primary reaction.

  • Nuclear Stability

    • The stability of an atom depends on the ratio and number of protons and neutrons, which may represent closed and filled quantum shells.
    • The stability of an atom depends on the ratio of its protons to its neutrons, as well as on whether it contains a "magic number" of neutrons or protons that would represent closed and filled quantum shells.
    • These quantum shells correspond to energy levels within the shell model of the nucleus.
    • Of the 254 known stable nuclides, only four have both an odd number of protons and an odd number of neutrons:
    • An atomic nucleus emits an alpha particle and thereby transforms ("decays") into an atom with a mass number smaller by four and an atomic number smaller by two.

  • The Uncertainty Principle

    • Heisenberg offered such an observer effect at the quantum level as a physical explanation of quantum uncertainty.
    • It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems and that it arises in quantum mechanics simply due to the matter-wave nature of all quantum objects.
    • Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it.
    • These include, for example, tests of number-phase uncertainty relations in superconducting or quantum optics systems.
    • One of the most-oft quoted results of quantum physics, this doozie forces us to reconsider what we can know about the universe.

  • The Wave Function

    • A wave function is a probability amplitude in quantum mechanics that describes the quantum state of a particle and how it behaves.
    • In quantum mechanics, a wave function is a probability amplitude describing the quantum state of a particle and how it behaves.
    • Typically, its values are complex numbers.
    • Although ψ is a complex number, |ψ|2 is a real number and corresponds to the probability density of finding a particle in a given place at a given time, if the particle's position is measured.
    • Furthermore, when we use the wave function to calculate an observation of the quantum system without meeting these requirements, there will not be finite or definite values to use (in this case the observation can take a number of values and can be infinite).