Physics:Quantum Schrödinger equation - Revision history

Harold: /* See also */

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See also

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	In the Copenhagen interpretation, the wave function represents information or probability amplitudes, and measurement involves probabilistic outcomes governed by the Born rule.<ref name=":0"/><ref name="omnes">{{cite book\|first=R. \|last=Omnès \|author-link=Roland Omnès \|title=The Interpretation of Quantum Mechanics \|publisher=Princeton University Press \|year=1994 \|isbn=978-0-691-03669-4 \|oclc=439453957}}</ref> Other interpretations, including many-worlds and Bohmian mechanics, retain the same Schrödinger equation while differing in how they understand physical reality and measurement.<ref>{{Cite book\|first=Jeffrey \|last=Barrett\|title=Stanford Encyclopedia of Philosophy\|publisher=Metaphysics Research Lab, Stanford University\|year=2018\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Everett's Relative-State Formulation of Quantum Mechanics}}</ref><ref>{{cite book\|chapter-url=https://plato.stanford.edu/entries/qm-bohm/ \|last=Goldstein \|first=Sheldon \|chapter=Bohmian Mechanics \|title=Stanford Encyclopedia of Philosophy \|year=2017 \|editor-first1=Edward N. \|editor-last=Zalta \|publisher=Metaphysics Research Lab, Stanford University}}</ref>		In the Copenhagen interpretation, the wave function represents information or probability amplitudes, and measurement involves probabilistic outcomes governed by the Born rule.<ref name=":0"/><ref name="omnes">{{cite book\|first=R. \|last=Omnès \|author-link=Roland Omnès \|title=The Interpretation of Quantum Mechanics \|publisher=Princeton University Press \|year=1994 \|isbn=978-0-691-03669-4 \|oclc=439453957}}</ref> Other interpretations, including many-worlds and Bohmian mechanics, retain the same Schrödinger equation while differing in how they understand physical reality and measurement.<ref>{{Cite book\|first=Jeffrey \|last=Barrett\|title=Stanford Encyclopedia of Philosophy\|publisher=Metaphysics Research Lab, Stanford University\|year=2018\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Everett's Relative-State Formulation of Quantum Mechanics}}</ref><ref>{{cite book\|chapter-url=https://plato.stanford.edu/entries/qm-bohm/ \|last=Goldstein \|first=Sheldon \|chapter=Bohmian Mechanics \|title=Stanford Encyclopedia of Philosophy \|year=2017 \|editor-first1=Edward N. \|editor-last=Zalta \|publisher=Metaphysics Research Lab, Stanford University}}</ref>

	~~== See also ==~~

	* Dirac equation
	* Klein–Gordon equation
	* Particle in a box
	* [[Physics:Quantum harmonic oscillator\|Quantum harmonic oscillator]]
	* density matrices
	* Interpretations of quantum mechanics
	* Probability current
	* Schrödinger picture
	== Notes ==		== Notes ==

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	=== Hydrogen atom ===		=== Hydrogen atom ===
	The Schrödinger equation for the electron in a [[Physics:~~Hydrogen atom~~\|hydrogen atom]] is		The Schrödinger equation for the electron in a [[Physics:Quantum atoms/hydrogen\|hydrogen atom]] is
	<math display="block"> E \psi = -\frac{\hbar^2}{2\mu}\nabla^2\psi - \frac{q^2}{4\pi\varepsilon_0 r}\psi.</math>		<math display="block"> E \psi = -\frac{\hbar^2}{2\mu}\nabla^2\psi - \frac{q^2}{4\pi\varepsilon_0 r}\psi.</math>

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	{{Short description\|Equation governing the wave function of a quantum-mechanical system}}~~Book I~~		{{Short description\|Equation governing the wave function of a quantum-mechanical system}}

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	'''Schrödinger equation''' ~~is a Book I topic in~~ the ~~Quantum Collection. The~~ Schrödinger equation is the fundamental equation of nonrelativistic quantum mechanics. It governs the time evolution of the wave function of a quantum-mechanical system and provides the mathematical basis for predicting measurable quantities such as probability densities, energies, and stationary states. It was introduced by Erwin Schrödinger in 1925–1926 and became one of the central achievements in the development of modern physics. The Schrödinger equation is the fundamental equation of nonrelativistic quantum mechanics. It governs the time evolution of the wave function of a quantum-mechanical system and provides the mathematical basis for predicting measurable quantities such as probability densities, energies, and stationary states. ~~It was introduced by Erwin~~ Schrödinger in ~~1925–1926 and became one~~ of ~~the central achievements~~ in ~~the development of modern physics.{{cite journal \| last = Schrödinger \| first = E~~.		'''Schrödinger equation''' the Schrödinger equation is the fundamental equation of nonrelativistic quantum mechanics. It governs the time evolution of the wave function of a quantum-mechanical system and provides the mathematical basis for predicting measurable quantities such as probability densities, energies, and stationary states. It was introduced by Erwin Schrödinger in 1925–1926 and became one of the central achievements in the development of modern physics. The Schrödinger equation is the fundamental equation of nonrelativistic quantum mechanics. It governs the time evolution of the wave function of a quantum-mechanical system and provides the mathematical basis for predicting measurable quantities such as probability densities, energies, and stationary states. Conceptually, the Schrödinger equation plays a role in quantum mechanics analogous to that of Newton's second law in classical mechanics.
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	* [[Physics:Schrödinger picture\|Schrödinger picture]]		* [[Physics:Schrödinger picture\|Schrödinger picture]]
	== Notes ==		== Notes ==

			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	{{reflist\|group=note}}		{{reflist\|group=note}}

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	{{Quantum article nav\|previous=Physics:Quantum Time evolution\|previous label=Time evolution\|next=Physics:Quantum Time-dependent Schrödinger equation\|next label=Time-dependent Schrödinger equation}}		{{Quantum article nav\|previous=Physics:Quantum Time evolution\|previous label=Time evolution\|next=Physics:Quantum Time-dependent Schrödinger equation\|next label=Time-dependent Schrödinger equation}}