quantum field theory

Examples of quantum field theory in the following topics:

• 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.

• 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:

• Implications of Quantum Mechanics

  • The field of quantum mechanics has been enormously successful in explaining many of the features of our world.
  • Quantum mechanics has also strongly influenced string theory.
  • The application of quantum mechanics to chemistry is known as quantum chemistry.
  • 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

• 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.

• Philosophical Implications

  • According to this interpretation, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but instead must be considered a final renunciation of the classical idea of causality.
  • Albert Einstein (shown in , himself one of the founders of quantum theory) disliked this loss of determinism in measurement in the Copenhagen interpretation.
  • Einstein held that there should be a local hidden variable theory underlying quantum mechanics and, consequently, that the present theory was incomplete.
  • John Bell showed by Bell's theorem that this "EPR" paradox led to experimentally testable differences between quantum mechanics and local realistic theories.
  • Experiments have been performed confirming the accuracy of quantum mechanics, thereby demonstrating that the physical world cannot be described by any local realistic theory.

• 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.

• Which Methodology is "Correct?"

  • To understand and contribute to any field of knowledge, it is necessary to be aware of the methodology(ies) that have guided the development of accepted ideas, hypotheses, theories, concepts, tools, values and ideologies that are used within that discipline.
  • Methodological problems apply to all knowledge including Newtonian mechanics, the theory of relativity and quantum mechanics as well as economics.
  • Modern economic theory has a long tradition of following a "modernist" methodology characterized by a strong faith in empiricism and rationalism.
  • Within modern economics, knowledge is believed to be advanced by inductive or empirical investigations that can verify (or fail to falsify) "positive" concepts, hypothesis, theories or models developed by deductive or rationalist logic.

• 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.