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- Introduction_to_eigenstates abstract "Because of the uncertainty principle, statements about both the position and momentum of particles can only assign a probability that the position or momentum will have some numerical value. The uncertainty principle also says that eliminating uncertainty about position maximises uncertainty about momentum, and eliminating uncertainty about momentum maximizes uncertainty about position. A probability distribution assigns probabilities to all possible values of position and momentum. Schrödinger's wave equation gives wavefunction solutions, the squares of which are probabilities of where the electron might be, just as Heisenberg's probability distribution does.In the everyday world, it is natural and intuitive to think of every object being in its own eigenstate. This is another way of saying that every object appears to have a definite position, a definite momentum, a definite measured value, and a definite time of occurrence. However, the uncertainty principle says that it is impossible to measure the exact value for the momentum of a particle like an electron, given that its position has been determined at a given instant. Likewise, it is impossible to determine the exact location of that particle once its momentum has been measured at a particular instant.Therefore it became necessary to formulate clearly the difference between the state of something that is uncertain in the way just described, such as an electron in a probability cloud, and the state of something having a definite value. When an object can definitely be "pinned down" in some respect, it is said to possess an eigenstate. As stated above, when the wavefunction collapses because the position of an electron has been determined, the electron's state becomes an "eigenstate of position", meaning that its position has a known value, an eigenvalue of the eigenstate of position.The word "eigenstate" is derived from the German/Dutch word "eigen", meaning "inherent" or "characteristic". An eigenstate is the measured state of some object possessing quantifiable characteristics such as position, momentum, etc. The state being measured and described must be observable (i.e. something such as position or momentum that can be experimentally measured either directly or indirectly), and must have a definite value, called an eigenvalue. ("Eigenvalue" also refers to a mathematical property of square matrices, a usage pioneered by the mathematician David Hilbert in 1904. Such matrices are called self-adjoint operators, and represent observables in quantum mechanics)".
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- Introduction_to_eigenstates wikiPageWikiLink Atomic_orbital.
- Introduction_to_eigenstates wikiPageWikiLink Category:Quantum_mechanics.
- Introduction_to_eigenstates wikiPageWikiLink David_Hilbert.
- Introduction_to_eigenstates wikiPageWikiLink Eigenstate.
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- Introduction_to_eigenstates wikiPageWikiLink Eigenvalues_and_eigenvectors.
- Introduction_to_eigenstates wikiPageWikiLink Electron.
- Introduction_to_eigenstates wikiPageWikiLink Electron_cloud.
- Introduction_to_eigenstates wikiPageWikiLink Momentum.
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- Introduction_to_eigenstates wikiPageWikiLink Quantum_state.
- Introduction_to_eigenstates wikiPageWikiLink Schrxc3xb6dingers_wave_equation.
- Introduction_to_eigenstates wikiPageWikiLink Schrödinger_equation.
- Introduction_to_eigenstates wikiPageWikiLink Self-adjoint_operator.
- Introduction_to_eigenstates wikiPageWikiLink Square_matrices.
- Introduction_to_eigenstates wikiPageWikiLink Square_matrix.
- Introduction_to_eigenstates wikiPageWikiLink Superposition_principle.
- Introduction_to_eigenstates wikiPageWikiLink Uncertainty_principle.
- Introduction_to_eigenstates wikiPageWikiLink Werner_Heisenberg.
- Introduction_to_eigenstates wikiPageWikiLinkText "Introduction to eigenstates".
- Introduction_to_eigenstates wikiPageWikiLinkText "eigenstate".
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- Introduction_to_eigenstates wikiPageUsesTemplate Template:Introductory_article.
- Introduction_to_eigenstates wikiPageUsesTemplate Template:Reflist.
- Introduction_to_eigenstates subject Category:Quantum_mechanics.
- Introduction_to_eigenstates type Article.
- Introduction_to_eigenstates type List.
- Introduction_to_eigenstates type Article.
- Introduction_to_eigenstates type List.
- Introduction_to_eigenstates type Mechanic.
- Introduction_to_eigenstates type Physic.
- Introduction_to_eigenstates comment "Because of the uncertainty principle, statements about both the position and momentum of particles can only assign a probability that the position or momentum will have some numerical value. The uncertainty principle also says that eliminating uncertainty about position maximises uncertainty about momentum, and eliminating uncertainty about momentum maximizes uncertainty about position. A probability distribution assigns probabilities to all possible values of position and momentum.".
- Introduction_to_eigenstates label "Introduction to eigenstates".
- Introduction_to_eigenstates sameAs Q6058958.
- Introduction_to_eigenstates sameAs Q6058958.
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