FACTOID # 74: More than a third of the time, Icelanders don't show up for work. Perhaps that's why they're the world's happiest nation.
 
 Home   Encyclopedia   Statistics   Countries A-Z   Flags   Maps   Education   Forum   FAQ   About 
 
WHAT'S NEW
RECENT ARTICLES
More Recent Articles »
 

FACTS & STATISTICS    Simple view

  1. Select countries to view: (hold down Control key and click to select several)

     

     

    Compare:

     

     

  1. Select fact or statistic: (* = graphable)

     

     

     

  2. (OPTIONAL) Compare to statistic: (both need to be graphable)

     

     

     

  3. View result as:

     

       
(OR) SEARCH ALL encyclopedia, stats & forums:   

Encyclopedia > Pauli equation
Quantum physics
Quantum mechanics

Introduction to...
Mathematical formulation of... Image File history File links Schrödinger_cat. ... Fig. ... Quantum mechanics (or quantum theory) is a physical science dealing with the behaviour of matter and waves on the scale of atoms and subatomic particles. ... The mathematical formulation of quantum mechanics is the body of mathematical formalisms which permits a rigorous description of quantum mechanics. ...

Fundamental concepts

Decoherence · Interference
Uncertainty · Exclusion
Transformation theory
Ehrenfest theorem Measurement In quantum mechanics, quantum decoherence is the mechanism by which quantum systems interact with their environments to exhibit probabilistically additive behavior - a feature of classical physics - and give the appearance of wavefunction collapse. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ... In quantum physics, the Heisenberg uncertainty principle is a mathematical limit on the accuracy with which it is possible to measure everything there is to know about a physical system. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. ... The term transformation theory refers to a procedure used by P. A. M. Dirac in his early formulation of quantum theory, from around 1927. ... The Ehrenfest theorem, named after Paul Ehrenfest, relates the time derivative of the expectation value for a quantum mechanical operator to the commutator of that operator with the Hamiltonian of the system. ... The framework of quantum mechanics requires a careful definition of measurement, and a thorough discussion of its practical and philosophical implications. ...

Experiments

Double-slit experiment
Davisson-Germer experiment
Stern–Gerlach experiment
EPR paradox · Schrodinger's Cat Double-slit diffraction and interference pattern The double-slit experiment consists of letting light diffract through two slits producing fringes or wave-like patterns on a screen. ... In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline Nickel target. ... In quantum mechanics, the Stern–Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated experiment in 1920 on deflection of particles, often used to illustrate basic principles of quantum mechanics. ... In quantum mechanics, the EPR paradox is a thought experiment which challenged long-held ideas about the relation between the observed values of physical quantities and the values that can be accounted for by a physical theory. ... Schrödingers cat is a seemingly paradoxical thought experiment devised by Erwin Schrödinger that attempts to illustrate the incompleteness of the theory of quantum mechanics when going from subatomic to macroscopic systems. ...

Equations

Schrödinger equation
Pauli equation
Klein-Gordon equation
Dirac equation In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... The Klein-Gordon equation (Klein-Fock-Gordon equation or sometimes Klein-Gordon-Fock equation) is the relativistic version of the Schrödinger equation. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...

Advanced theories

Quantum field theory
Quantum electrodynamics
Quantum chromodynamics
Quantum gravity
Feynman diagram Quantum field theory (QFT) is the application of quantum mechanics to fields. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... Quantum chromodynamics (QCD) is the theory of the strong interaction, a fundamental force describing the interactions of the quarks and gluons found in nucleons (such as the proton and neutron). ... This article or section does not cite its references or sources. ... In this Feynman diagram, an electron and positron annihilate and become a quark-antiquark pair. ...

Interpretations

Copenhagen · Quantum logic
Hidden variables · Transactional
Many-worlds · Ensemble
Consistent histories · Relational
Consciousness causes collapse
Orchestrated objective reduction The Copenhagen interpretation is an interpretation of quantum mechanics formulated by Niels Bohr and Werner Heisenberg while collaborating in Copenhagen around 1927. ... In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... In physics, a hidden variable theory is urged by a minority of physicists who argue that the statistical nature of quantum mechanics implies that quantum mechanics is incomplete; it is really applicable only to ensembles of particles; new physical phenomena beyond quantum mechanics are needed to explain an individual event. ... The transactional interpretation of quantum mechanics (TIQM) by Professor John Cramer is an unusual interpretation of quantum mechanics that describes quantum interactions in terms of a standing wave formed by retarded (forward in time) and advanced (backward in time) waves. ... The many-worlds interpretation of quantum mechanics or MWI (also known as the relative state formulation, theory of the universal wavefunction, many-universes interpretation, Oxford interpretation or many worlds), is an interpretation of quantum mechanics that claims to resolve all the paradoxes of quantum theory by allowing every possible outcome... The Ensemble Interpretation, or Statistical Interpretation of Quantum Mechanics, is an interpretation that can be viewed as a minimalist interpretation. ... In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. ... // Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, the state is the relation between the observer and the system. ... Consciousness causes collapse is the theory that observation by a conscious observer is responsible for the wavefunction collapse in quantum mechanics. ... Orch OR (“Orchestrated Objective Reduction”) is a theory of consciousness put forth in the mid-1990s by British theoretical physicist Sir Roger Penrose and American anesthesiologist Stuart Hameroff. ...

Scientists

Planck · Schrödinger
Heisenberg · Bohr · Pauli
· Dirac · Bohm · Born
de Broglie · von Neumann
Einstein · Feynman
Everett · Others Max Karl Ernst Ludwig Planck (April 23, 1858 – October 4, 1947) was a German physicist. ... Erwin Rudolf Josef Alexander Schrödinger (August 12, 1887 – January 4, 1961) was an Austrian physicist who achieved fame for his contributions to quantum mechanics, especially the Schrödinger equation, for which he received the Nobel Prize in 1933. ... Werner Karl Heisenberg (December 5, 1901 – February 1, 1976) was a celebrated German physicist and Nobel laureate, one of the founders of quantum mechanics, and acknowledged to be one of the most important physicists of the twentieth century. ... Niels (Henrik David) Bohr (October 7, 1885 – November 18, 1962) was a Danish physicist who made fundamental contributions to understanding atomic structure and quantum mechanics. ... This article is about Austrian-Swiss physicist Wolfgang Pauli. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... David Bohm. ... Max Born (December 11, 1882 in Breslau – January 5, 1970 in Göttingen) was a mathematician and physicist. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892–March 19, 1987), was a French physicist and Nobel Prize laureate. ... John von Neumann (Hungarian Margittai Neumann János Lajos) (born December 28, 1903 in Budapest, Austria-Hungary; died February 8, 1957 in Washington D.C., United States) was a Hungarian-born mathematician and polymath who made contributions to quantum physics, functional analysis, set theory, topology, economics, computer science, numerical analysis... Albert Einstein ( ) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist who is widely considered one of the greatest physicists of all time. ... Richard Phillips Feynman (May 11, 1918 – February 15, 1988; surname pronounced ) was an American physicist known for expanding the theory of quantum electrodynamics, the physics of the superfluidity of supercooled liquid helium, and particle theory. ... Hugh Everett III (November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation of quantum physics, which he called his relative state formulation. ... Below is a list of famous physicists. ...

This box: view  talk  edit

The Pauli equation is a Schrödinger equation which handles spin. It is the non-relativistic border case of the Dirac equation. In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the space- and time-dependence of quantum mechanical systems. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...


Details

The time dependent linear Pauli equation :

where
is the momentum
c is the speed of light
are the Pauli matrices
is the Pauli-Spinor

Both spinor components satisfy the Schrödinger-Equation. This means that the system is as to the additional degree of freedom, degenerated. The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation in a vacuum, not just visible light. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...


With an external electromagnetic field the full Pauli equation reads:

It shows the energetic disperment in a magnetic field as can be viewed in the anomal Zeeman effect. The Zeeman effect (IPA ) is the splitting of a spectral line into several components in the presence of a magnetic field. ...


Example



 

COMMENTARY     


Share your thoughts, questions and commentary here
Your name
Your comments
Please enter the 5-letter protection code

Want to know more?
Search encyclopedia, statistics and forums:

 


Lesson Plans | Student Area | Student FAQ | Reviews | Press Releases |  Feeds | Contact
The Wikipedia article included on this page is licensed under the GFDL.
Images may be subject to relevant owners' copyright.
All other elements are (c) copyright NationMaster.com 2003-5. All Rights Reserved.
Usage implies agreement with terms.