quantum theory

Examples of quantum theory in the following topics:

• 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.

• 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.
  • where n = 1, 2, 3, ... is called the principal quantum number and ħ = h/2π.
  • Like Einstein's theory of the photoelectric effect, Bohr's formula assumes that during a quantum jump, a discrete amount of energy is radiated.
  • 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-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.

• Implications of Quantum Mechanics

  • Quantum mechanics has also strongly influenced string theory.
  • The application of quantum mechanics to chemistry is known as quantum chemistry.
  • Researchers are currently seeking robust methods of directly manipulating quantum states.
  • 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

• Planck's Quantum Hypothesis and Black Body Radiation

  • Planck's quantum hypothesis is a pioneering work, heralding advent of a new era of modern physics and quantum theory.
  • Predictions based on classical theories failed to explain black body spectra observed experimentally, especially at shorter wavelength.
  • Although Planck's derivation is beyond the scope of this section (it will be covered in Quantum Mechanics), Planck's law may be written:
  • Planck's quantum hypothesis is one of the breakthroughs in the modern physics.
  • Black line is a prediction of a classical theory for an object at 5,000K, showing catastropic discrepancy at shorter wavelengh.

• 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.

• 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.

• 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:

• 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.