quantum field theory

(noun)

Provides a theoretical framework for constructing quantum mechanical models of systems classically represented by an infinite number of degrees of freedom, that is, fields and many-body systems.

Related Terms

Examples of quantum field theory in the following topics:

  • Description of the Hydrogen Atom

    • The hydrogen atom (consisting of one proton and one electron, not the diatomic form H2) has special significance in quantum mechanics and quantum field theory as a simple two-body problem physical system that has yielded many simple analytical solutions in closed-form.
    • 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.
    • Empirically, it is useful to group the fundamental constants into Rydbergs, which gives the much simpler equation below that turns out to be identical to that predicted by Bohr theory:

  • The Bohr Model

    • The quantum theory from the period between Planck's discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory.
    • Like Einstein's theory of the photoelectric effect, Bohr's formula assumes that during a quantum jump, a discrete amount of energy is radiated.
    • However, unlike Einstein, Bohr stuck to the classical Maxwell theory of the electromagnetic field.
    • This marks the birth of the correspondence principle, requiring quantum theory to agree with the classical theory only in the limit of large quantum numbers.
    • The Bohr-Kramers-Slater theory (BKS theory) is a failed attempt to extend the Bohr model, which violates the conservation of energy and momentum in quantum jumps, with the conservation laws only holding on average.

  • Quantum Numbers

    • Quantum numbers provide a numerical description of the orbitals in which electrons reside.
    • Formally, the dynamics of any quantum system are described by a quantum Hamiltonian (H) applied to the wave equation.
    • The most prominent system of nomenclature spawned from the molecular orbital theory of Friedrich Hund and Robert S.
    • The average distance increases with n, thus quantum states with different principal quantum numbers are said to belong to different shells.
    • 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.

  • 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.
    • Possibly the first systematic attempt at a mathematical theory for quantum measurement was developed by John von Neumann.
    • 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.

  • 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.
    • The quantum yield of these products is less than 0.2, indicating there are radiative (fluorescence & phosphorescence) and non-radiative return pathways (green arrow).
    • Several secondary radical reactions then follow (shown in the gray box), making it difficult to assign a quantum yield to the primary reaction.

  • Planck's Quantum Theory

    • As a result of these observations, physicists articulated a set of theories now known as quantum mechanics.
    • In some ways, quantum mechanics completely changed the way physicists viewed the universe, and it also marked the end of the idea of a clockwork universe (the idea that universe was predictable).
    • Max Planck named this minimum amount the "quantum," plural "quanta," meaning "how much."
    • One photon of light carries exactly one quantum of energy.
    • Planck is considered the father of the Quantum Theory.

  • Linear Combination of Atomic Orbitals (LCAO)

    • An LCAO approximation is a quantum superposition of atomic orbitals, used to calculate molecular orbitals in quantum chemistry.
    • These models provide a simple model of molecule bonding, understood through molecular orbital theory.
    • A linear combination of atomic orbitals, or LCAO, is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry.
    • In quantum mechanics, electron configurations of atoms are described as wave functions.

  • The Pauli Exclusion Principle

    • The Pauli exclusion principle, formulated by Austrian physicist Wolfgang Pauli in 1925, states that no two fermions of the same kind may simultaneously occupy the same quantum state.
    • In the theory of quantum mechanics, fermions are described by antisymmetric states.
    • In contrast, particles with integer spin (bosons) have symmetric wave functions; unlike fermions, bosons may share the same quantum states.
    • Electrons, being fermions, cannot occupy the same quantum state, so electrons have to "stack" within an atom—they have different spins while at the same place.
    • As spin is part of the quantum state of the electron, the two electrons are in different quantum states and do not violate the Pauli exclusion principle.

  • Diamagnetism and Paramagnetism

    • Any time two electrons share the same orbital, their spin quantum numbers have to be different.
    • In order to decide whether electron spins cancel, add their spin quantum numbers together.
    • Diamagnetic atoms are not attracted to a magnetic field, but rather are slightly repelled.
    • Just as diamagnetic atoms are slightly repelled from a magnetic field, paramagnetic atoms are slightly attracted to a magnetic field.
    • Paramagnetic properties are due to the realignment of the electron paths caused by the external magnetic field.

  • Electron Configurations and Magnetic Properties of Ions

    • In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule in atomic or molecular orbitals.
    • According to the laws of quantum mechanics, a certain energy is associated with each electron configuration.
    • Under certain conditions, electrons can move from one orbital to another by emission or absorption of a quantum of energy, in the form of a photon.
    • Magnetism is a property of materials that respond to an applied magnetic field.
    • However, all materials are influenced differently by the presence of a magnetic field.