relativistic quantum mechanics

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.