Physics:Quantum number - Revision history

WikiHarold: Remove leading BOM from Quantum page

2026-05-24T00:57:18Z

Remove leading BOM from Quantum page

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WikiHarold: Remove red links introduced by reference repair

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	== Spin–orbit coupled systems ==		== Spin–orbit coupled systems ==
	When one takes the spin–orbit interaction into consideration, the {{mvar\|L}} and {{mvar\|S}} operators no longer commute with the Hamiltonian, and the eigenstates of the system no longer have well-defined orbital angular momentum and spin. Thus another set of quantum numbers should be used. This set includes<ref>{{cite book\|title=Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry \|volume=1 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977 \|isbn=0-19-855129-0}} </ref><ref name="Atkins 1977">{{cite book\|title=Molecular Quantum Mechanics Part III: An Introduction to Quantum Chemistry \|volume=2 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977~~}}{{ISBN missing}}{{page needed\|date=February 2019~~}}</ref>		When one takes the spin–orbit interaction into consideration, the {{mvar\|L}} and {{mvar\|S}} operators no longer commute with the Hamiltonian, and the eigenstates of the system no longer have well-defined orbital angular momentum and spin. Thus another set of quantum numbers should be used. This set includes<ref>{{cite book\|title=Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry \|volume=1 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977 \|isbn=0-19-855129-0}} </ref><ref name="Atkins 1977">{{cite book\|title=Molecular Quantum Mechanics Part III: An Introduction to Quantum Chemistry \|volume=2 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977}}</ref>
	# The total angular momentum quantum number: <math display="block">		# The total angular momentum quantum number: <math display="block">
	j = \|\ell \pm s\|,		j = \|\ell \pm s\|,
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	\|m_\ell + m_s\| \leq j.		\|m_\ell + m_s\| \leq j.
	</math>		</math>
	# Parity{{br}}This is the eigenvalue under reflection: positive (+1) for states which came from even {{mvar\|{{ell}}}} and negative (−1) for states which came from odd {{mvar\|{{ell}}}}. The former is also known as '''even parity''' and the latter as '''odd parity''', and is given by<math display=block>		# Parity<br />This is the eigenvalue under reflection: positive (+1) for states which came from even {{mvar\|{{ell}}}} and negative (−1) for states which came from odd {{mvar\|{{ell}}}}. The former is also known as '''even parity''' and the latter as '''odd parity''', and is given by<math display=block>
	P = (-1)^\ell .</math>		P = (-1)^\ell .</math>

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:47Z

Restore missing Quantum reference definitions

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	== Spin–orbit coupled systems ==		== Spin–orbit coupled systems ==
	When one takes the spin–orbit interaction into consideration, the {{mvar\|L}} and {{mvar\|S}} operators no longer commute with the Hamiltonian, and the eigenstates of the system no longer have well-defined orbital angular momentum and spin. Thus another set of quantum numbers should be used. This set includes<ref>{{cite book\|title=Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry \|volume=1 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977 \|isbn=0-19-855129-0}} </ref><ref name="Atkins 1977">{{cite book\|title=Molecular Quantum Mechanics Part III: An Introduction to Quantum Chemistry \|volume=2 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977}}{{ISBN missing}}{{page needed\|date=February 2019} # The total angular momentum quantum number: <math display="block">		When one takes the spin–orbit interaction into consideration, the {{mvar\|L}} and {{mvar\|S}} operators no longer commute with the Hamiltonian, and the eigenstates of the system no longer have well-defined orbital angular momentum and spin. Thus another set of quantum numbers should be used. This set includes<ref>{{cite book\|title=Molecular Quantum Mechanics Parts I and II: An Introduction to Quantum Chemistry \|volume=1 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977 \|isbn=0-19-855129-0}} </ref><ref name="Atkins 1977">{{cite book\|title=Molecular Quantum Mechanics Part III: An Introduction to Quantum Chemistry \|volume=2 \|first=P. W. \|last=Atkins \|publisher=Oxford University Press \|date=1977}}{{ISBN missing}}{{page needed\|date=February 2019}}</ref>
			# The total angular momentum quantum number: <math display="block">
	j = \|\ell \pm s\|,		j = \|\ell \pm s\|,
	</math> which gives the total angular momentum through the relation <math display=block>		</math> which gives the total angular momentum through the relation <math display=block>
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	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	== References ==		= References =
	{{reflist}}		{{reflist}}

WikiHarold: Remove imported red links from Quantum page

2026-05-23T23:48:07Z

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	{{Redirect\|Q-number\|the Q-theory concept\|Q-analog\|the number format\|Q (number format)}}		{{Redirect\|Q-number\|the Q-theory concept\|Q-analog\|the number format\|Q (number format)}}
	~~{{Quantum mechanics\|fundamentals}}~~
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	{{Electron configuration navbox}}		{{Electron configuration navbox}}
	~~[[Category:Quantum measurement\| ]]~~
	~~[[Category:Physical quantities]]~~
	~~[[Category:Quantum numbers]]~~

	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Physics:Quantum number\|1}}		{{Sourceattribution\|Physics:Quantum number\|1}}

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	{{Electron configuration navbox}}		{{Electron configuration navbox}}
	~~{{Quantum mechanics topics}}~~

	[[Category:Quantum measurement\| ]]		[[Category:Quantum measurement\| ]]
	[[Category:Physical quantities]]		[[Category:Physical quantities]]

WikiHarold: Use Quantum See also index module

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	== Multiplicative quantum numbers ==		== Multiplicative quantum numbers ==
	Most conserved quantum numbers are additive, so in an elementary particle reaction, the ''sum'' of the quantum numbers should be the same before and after the reaction. However, some, usually called ''parities'', are multiplicative; i.e., their ''product'' is conserved. All multiplicative quantum numbers belong to a symmetry (like parity) in which applying the symmetry transformation twice is equivalent to doing nothing (involution).		Most conserved quantum numbers are additive, so in an elementary particle reaction, the ''sum'' of the quantum numbers should be the same before and after the reaction. However, some, usually called ''parities'', are multiplicative; i.e., their ''product'' is conserved. All multiplicative quantum numbers belong to a symmetry (like parity) in which applying the symmetry transformation twice is equivalent to doing nothing (involution).

	~~== See also ==~~
	* Electron configuration
	~~{{clear}}~~

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

Maintenance script: Normalize quantum page header order

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	{{Quantum article nav\|previous=Physics:Quantum Hydrogen atom\|previous label=Hydrogen atom\|next=Physics:Quantum Multi-electron atoms\|next label=Multi-electron atoms}}		{{Quantum article nav\|previous=Physics:Quantum Hydrogen atom\|previous label=Hydrogen atom\|next=Physics:Quantum Multi-electron atoms\|next label=Multi-electron atoms}}

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	{{Quantum article nav\|previous=Physics:Quantum Hydrogen atom\|previous label=Hydrogen atom\|next=Physics:Quantum Multi-electron atoms\|next label=Multi-electron atoms}}		{{Quantum article nav\|previous=Physics:Quantum Hydrogen atom\|previous label=Hydrogen atom\|next=Physics:Quantum Multi-electron atoms\|next label=Multi-electron atoms}}