relativistic quantum mechanics

(noun)

a theoretical framework for constructing quantum mechanical models of fields and many-body systems

Related Terms

  • cryptography
  • string theory

Examples of relativistic quantum mechanics in the following topics:

  • 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.
    • Relativistic quantum mechanics can, in principle, mathematically describe most of chemistry.
    • 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.
  • 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.
    • Bohr's results for the frequencies and underlying energy values were confirmed by the full quantum-mechanical analysis which uses the Schrödinger equation, as was shown in 1925–1926.
    • The solution of the Schrödinger equation goes much further than the Bohr model, because it also yields the shape of the electron's wave function (orbital) for the various possible quantum-mechanical states, thus explaining the anisotropic character of atomic bonds.
    • The quantity in square brackets arises from relativistic (spin-orbit) coupling interactions.
    • Identify the unique features of the hydrogen atom that make it important for calculations in quantum mechanics
  • Atomic Structure

    • We also derived some important relationships between how atoms emit and absorb radiation, but to understand atomic processes in detail we will have to treat the electrons quantum mechanically.
    • In quantum mechanics we characterize the state of a particles (or group of particles) by the wavefunction ($\Psi$).
    • We have neglect the spin of the electrons, relativistic and nuclear effects.
  • Philosophical Implications

    • Since its inception, many counter-intuitive aspects of quantum mechanics have provoked strong philosophical debates.
    • This is due to the quantum mechanical principle of wave function collapse.
    • One of the most bizarre aspect of the quantum mechanics is known as quantum entanglement.
    • According to the Copenhagen interpretation of quantum mechanics, their shared state is indefinite until measured.
    • Formulate the Copenhagen interpretation of the probabilistic nature of quantum mechanics
  • Relativistic Kinetic Energy

    • In classical mechanics, the kinetic energy of an object depends on the mass of a body as well as its speed.
    • Indeed, the relativistic expression for kinetic energy is:
    • $KE = mc^2-m_0c^2$, where m is the relativistic mass of the object and m0 is the rest mass of the object.
    • At a low speed ($v << c$), the relativistic kinetic energy may be approximated well by the classical kinetic energy.
    • Compare classical and relativistic kinetic energies for objects at speeds much less and approaching the speed of light
  • The Uncertainty Principle

    • In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position (x) and momentum (p), can be known simultaneously.
    • 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.
  • Indeterminacy and Probability Distribution Maps

    • Quantum mechanics provides a recipe for calculating this probability distribution.
    • 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.
  • 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.
    • The laws of quantum mechanics (the Schrödinger equation) describe how the wave function evolves over time.
    • This figure shows some trajectories of a harmonic oscillator (a ball attached to a spring) in classical mechanics (A-B) and quantum mechanics (C-H).
    • In quantum mechanics (C-H), the ball has a wave function, which is shown with its real part in blue and its imaginary part in red.
  • A Physical Aside: Einstein coefficients

    • Fermi's Golden Rule relates the cross-section for a process to a quantum mechanical matrix element and the phase space available for the products.
    • Because quantum mechanics for the most part is time reversible, the cross-section for the forward and reverse reactions are related.
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