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• Wave_function abstract "A wave function or wavefunction (also named a state function) in quantum mechanics describes the quantum state of a system of one or more particles, and contains all the information about the system. Quantities associated with measurements, like the average momentum of a particle, are derived from the wavefunction. Thus it is a central quantity in quantum mechanics. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi). The Schrödinger equation determines how the wave function evolves over time, that is, the wavefunction is the solution of the Schrödinger equation. The wave function behaves qualitatively like other waves, like water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality.The wave function for a given system does not have a unique representation. Most commonly, it is taken to be a function of all the position coordinates of the particles and time, that is, the wavefunction is in "position space". However, we could also consider a wave function in "momentum space"; a function of all the momenta of the particles and time instead. In general, the wave function of a system is a function of continuous and discrete variables characterizing the system's degrees of freedom, and there is one wavefunction for the entire system, not a separate wavefunction for each particle in the system. Elementary particles, like electrons, have spin, and the wavefunction must include this fundamental property as an intrinsic degree of freedom. The wave function is spinorial for fermions, namely particles with half-integer spin (1/2, 3/2, 5/2, ...), or tensorial for bosons, particles with integer spin (0, 1, 2, 3, ...).In most treatments of quantum mechanics, the wavefunction is complex-valued. In one important interpretation of quantum mechanics called the Copenhagen interpretation, the modulus squared of the wavefunction, |ψ|2, is a real number interpreted as the probability density of finding a particle in a given place at a given time, if the particle's position is to be measured. Since the wavefunction is complex valued, only its relative phase and relative magnitude can be measured. It does not directly tell anything about the magnitudes or directions of measurable observables, one has to apply quantum operators to the wave function ψ and find the eigenvalues which correspond to sets of possible results of measurement. However, complex numbers are not necessarily used in all treatments. Louis de Broglie in his later years proposed a real-valued wave function connected to the complex wave function by a proportionality constant and developed the de Broglie–Bohm theory.The unit of measurement for ψ depends on the system. For one particle in three dimensions, its units are [length]−3/2. These unusual units are required so that an integral of |ψ|2 over a region of three-dimensional space is a unitless probability (the probability that the particle is in that region). For different numbers of particles and/or dimensions, the units may be different and can be found by dimensional analysis.".
• Wave_function thumbnail QuantumHarmonicOscillatorAnimation.gif?width=300.
• Wave_function wikiPageExternalLink lectnote.pdf.
• Wave_function wikiPageExternalLink normalize.html.
• Wave_function wikiPageExternalLink IdenticalParticlesRevisited.htm.
• Wave_function wikiPageExternalLink node34.html.
• Wave_function wikiPageExternalLink complexs.html.
• Wave_function wikiPageExternalLink node2.html.
• Wave_function wikiPageExternalLink about.
• Wave_function wikiPageID "145343".
• Wave_function wikiPageRevisionID "605369347".
• Wave_function align "right".
• Wave_function caption "Continuous components of a complex vector , which belongs to an uncountably infinite-dimensional Hilbert space; there are uncountably infinitely many x values and basis vectors .".
• Wave_function caption "Discrete components of a complex vector , which belongs to a countably infinite-dimensional Hilbert space; there are countably infinitely many values and basis vectors .".
• Wave_function caption "Standing waves for a particle in a box, examples of stationary states.".
• Wave_function caption "Travelling waves of a free particle.".
• Wave_function direction "vertical".
• Wave_function footer "Components of complex vectors plotted against index number; discrete and continuous . Two probability amplitudes out of infinitely many are highlighted.".
• Wave_function footer "The real parts of position and momentum wave functions and , and corresponding probability densities and , for one spin-0 particle in one or dimension. The wave functions shown are continuous, finite, single-valued and normalized. The colour opacity of the particles corresponds to the probability density of finding the particle at position or momentum .".
• Wave_function hasPhotoCollection Wave_function.
• Wave_function image "Continuous complex vector components.svg".
• Wave_function image "Discrete complex vector components.svg".
• Wave_function image "Quantum mechanics standing wavefunctions.svg".
• Wave_function image "Quantum mechanics travelling wavefunctions.svg".
• Wave_function width "225".
• Wave_function width "230".
• Wave_function width "402".
• Wave_function subject Category:Concepts_in_physics.
• Wave_function subject Category:Quantum_mechanics.
• Wave_function type Abstraction100002137.
• Wave_function type Cognition100023271.
• Wave_function type Concept105835747.
• Wave_function type Content105809192.
• Wave_function type FundamentalPhysicsConcepts.
• Wave_function type Idea105833840.
• Wave_function type PsychologicalFeature100023100.
• Wave_function comment "A wave function or wavefunction (also named a state function) in quantum mechanics describes the quantum state of a system of one or more particles, and contains all the information about the system. Quantities associated with measurements, like the average momentum of a particle, are derived from the wavefunction. Thus it is a central quantity in quantum mechanics. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi).".
• Wave_function label "Fonction d'onde".
• Wave_function label "Función de onda".
• Wave_function label "Funkcja falowa".
• Wave_function label "Funzione d'onda".
• Wave_function label "Função de onda".
• Wave_function label "Golffunctie".
• Wave_function label "Wave function".
• Wave_function label "Wellenfunktion".
• Wave_function label "Волновая функция".
• Wave_function label "دالة موجية".
• Wave_function label "波函数".
• Wave_function label "波動関数".
• Wave_function sameAs Vlnová_funkce.
• Wave_function sameAs Wellenfunktion.
• Wave_function sameAs Κυματοσυνάρτηση.
• Wave_function sameAs Función_de_onda.
• Wave_function sameAs Fonction_d'onde.
• Wave_function sameAs Funzione_d'onda.
• Wave_function sameAs 波動関数.
• Wave_function sameAs 파동_함수.
• Wave_function sameAs Golffunctie.
• Wave_function sameAs Funkcja_falowa.
• Wave_function sameAs Função_de_onda.
• Wave_function sameAs m.012gh4.
• Wave_function sameAs Q2362761.
• Wave_function sameAs Q2362761.
• Wave_function sameAs Wave_function.
• Wave_function wasDerivedFrom Wave_function?oldid=605369347.
• Wave_function depiction QuantumHarmonicOscillatorAnimation.gif.
• Wave_function isPrimaryTopicOf Wave_function.