Physics:Quantum Planck constant - Revision history

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	'''Planck constant''' ~~is a Book I topic in~~ the ~~Quantum Collection. The~~ Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation. Together with the reduced Planck constant, it is one of the central numerical anchors of quantum theory. The Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation.		'''Planck constant''' the Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation. Together with the reduced Planck constant, it is one of the central numerical anchors of quantum theory. The Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation. The Planck constant relates the energy of a quantum to the frequency of the associated radiation.
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	The Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation. Together with the reduced Planck constant, it is one of the central numerical anchors of quantum theory.		'''Planck constant''' is a Book I topic in the Quantum Collection. The Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation. Together with the reduced Planck constant, it is one of the central numerical anchors of quantum theory. The Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation.
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	== Appearance in quantum equations ==		== Appearance in quantum equations ==
	The constant appears in the [[Physics:Quantum Schrödinger equation\|Schrodinger equation]], [[Physics:Quantum Time evolution\|time evolution]], [[Physics:Quantum Observables and operators\|operators]], and [[Physics:Quantum Uncertainty principle\|uncertainty principle]].		The constant appears in the [[Physics:Quantum Schrödinger equation\|Schrodinger equation]], [[Physics:Quantum Time evolution\|time evolution]], [[Physics:Quantum Observables and operators\|operators]], and [[Physics:Quantum Uncertainty principle\|uncertainty principle]].

			== Description ==
			'''Planck constant''' is a matter-scale concept used to organize how quantum theory describes atoms, particles, fields, condensed matter, plasma, or spacetime-related systems. In the Quantum Collection it is placed by scale so the reader can move from materials and molecules down to subatomic degrees of freedom.

			== Quantum context ==
			At this scale, the relevant behavior is controlled by quantized states, interactions, conservation laws, and the way excitations or particles are observed. The concept is normally linked to measurable properties such as energy, momentum, charge, spin, spectra, scattering rates, or collective modes.

			== Role in the collection ==
			This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in [[Physics:Quantum mechanics\|quantum mechanics]].<ref name="matter-wiki">{{cite web \|url=https://en.wikipedia.org/wiki/Quantum_mechanics \|title=Quantum mechanics \|website=Wikipedia \|access-date=2026-05-20}}</ref>

	== See also ==		== See also ==

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 {{Quantum book backlink|Foundations}}
 The Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation. Together with the reduced Planck constant, it is one of the central numerical anchors of quantum theory.
 == Definition ==

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{{Short description|Fundamental quantum constant setting the scale of quantization, action, and quantum uncertainty}}
{{Quantum book backlink|Foundations}}

The Planck constant is the fundamental constant that relates the energy of a quantum to its frequency. It sets the scale at which quantum effects become important and appears throughout quantum mechanics, including wavefunctions, commutation relations, uncertainty relations, angular momentum, and the Schrodinger equation. Together with the reduced Planck constant, it is one of the central numerical anchors of quantum theory.

== Definition ==
The Planck constant relates the energy of a quantum to the frequency of the associated radiation. In the Quantum Collection it connects [[Physics:Quantum photon|photons]], [[Physics:Quantum electromagnetic field|electromagnetic radiation]], and [[Physics:Quantum methods/quantization|quantization]].

== Reduced Planck constant ==
The reduced Planck constant is the Planck constant divided by <math>2\pi</math>. It appears naturally in equations involving angular frequency, angular momentum, and quantum operators.

== Role in quantization ==
Quantization means that certain physical quantities occur in discrete values rather than arbitrary continuous amounts. The Planck constant sets the scale of those discrete steps in many quantum systems.

== Uncertainty and action ==
The Planck constant has the dimensions of action and appears in uncertainty relations. It helps determine when quantum effects are significant compared with classical behavior.

== Appearance in quantum equations ==
The constant appears in the [[Physics:Quantum Schrödinger equation|Schrodinger equation]], [[Physics:Quantum Time evolution|time evolution]], [[Physics:Quantum Observables and operators|operators]], and [[Physics:Quantum Uncertainty principle|uncertainty principle]].

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

== References ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Planck constant|1}}