relativistic quantum mechanics

(noun)

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

Related Terms

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.

  • 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 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.

  • The Bohr Model of the Atom

    • Bohr suggested that electrons in hydrogen could have certain classical motions only when restricted by a quantum rule.
    • Bohr's theory explained the atomic spectrum of hydrogen, made him instantly famous, and established new and broadly applicable principles in quantum mechanics.
    • The laws of classical mechanics predict that the electron should release electromagnetic radiation while orbiting a nucleus (according to Maxwell's equations, accelerating charge should emit electromagnetic radiation).
    • The significance of the Bohr model is that the laws of classical mechanics apply to the motion of the electron about the nucleus only when restricted by a quantum rule.
    • His many contributions to the development of atomic physics and quantum mechanics; his personal influence on many students and colleagues; and his personal integrity, especially in the face of Nazi oppression, earned him a prominent place in history.

  • 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.
    • 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.

  • Energies of Electron States

    • The energy levels of the hydrogen atom at this level of approximation simply depend on the quantum number $n$.
    • Actually, it is relativistic effects that remove this degeneracy.
    • Sometimes this shielding effect is stronger than the change in the principal quantum number so we have the following ordering of states
    • A second important fact is that because electrons are indistinguishable, the wave function of more than one electron must be antisymmetric with respect to interchange of any two electrons (within the axioms of non-relativistic QM it could have be symmetric, but one can prove in relativistic QM that the wavefunction must be antisymmetric—the spin-statistics theorem).
    • We can label the states by their quantum numbers, $n, l, m_l, m_s$ where $l < n$, $-l\leq m_l \leq l$, $m_s=\pm\frac{1}{2}$.