Transformation theory (quantum mechanics)

Quantum mechanics
$\sigma_x \sigma_p \ge \frac{\hbar}{2}$ Uncertainty principle
Introduction Glossary History
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Complementarity Decoherence Entanglement Energy level Measurement Nonlocality Quantum number State Superposition Symmetry Tunnelling Uncertainty Wave function (collapse)
Experiments Afshar Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Mach–Zehnder Popper Quantum eraser (delayed-choice) Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Heisenberg Interaction Matrix Phase-space Schrödinger Sum-over-histories (path integral)
Equations Dirac Klein–Gordon Pauli Rydberg Schrödinger
Interpretations Overview Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective collapse Bayesian Quantum logic Relational Stochastic Scale relativity Transactional
Advanced topics Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum information science Relativistic quantum mechanics Scattering theory Quantum statistical mechanics
Scientists Aharonov Bell Blackett Bloch Bohm Bohr Born Bose de Broglie Candlin Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger

The term transformation theory refers to a procedure and a "picture" used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927.^[1]

This "transformation" idea refers to the changes a quantum state undergoes in the course of time, whereby its vector "moves" between "positions" or "orientations" in its Hilbert space.^[2] Time evolution, quantum transitions, and symmetry transformations in Quantum mechanics may thus be viewed as the systematic theory of abstract, generalized rotations in this space of quantum state vectors.

Remaining in full use today, it would be regarded as a topic in the mathematics of Hilbert space, although, technically speaking, it is somewhat more general in scope. While the terminology is reminiscent of rotations of vectors in ordinary space, the Hilbert space of a quantum object is more general, and holds its entire quantum state.

(The term further sometimes evokes the wave-particle duality, according to which a particle (a "small" physical object) may display either particle or wave aspects, depending on the observational situation. Or, indeed, a variety of intermediate aspects, as the situation demands.)

References

↑ Dirac, P.A.M. (January 1927). "The Physical Interpretation of the Quantum Dynamics". Proceedings of the Royal Society of London. A 113 (765): 621–641. Bibcode:1927RSPSA.113..621D. doi:10.1098/rspa.1927.0012. Retrieved 4 October 2011.
↑ Dirac, P. A. M. (1930). The Principles of Quantum Mechanics, Cambridge University Press; Prugovecki, Eduard (2006). Quantum Mechanics in Hilbert Space, Second Edition (Dover Books on Physics) Paperback. ISBN 0486453278 .

This article is issued from Wikipedia - version of the Tuesday, June 09, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.