Estimation of nanomechanical quantisation - Revision history

Apm: /* Estimations */

2021-06-26T00:34:22Z

Estimations

← Older revision		Revision as of 02:34, 26 June 2021
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	Following: zero point energies (need not be equal but are similar in size to quanta)		Following: zero point energies (need not be equal but are similar in size to quanta)

			{{wikitodo\|give concrete examples with numbers}} <br>
			See: [[Nanomechanics is barely mechanical quantummechanics]]

	== Quantisation in rotation (angular momentum) ==		== Quantisation in rotation (angular momentum) ==

2021-05-30T14:56:04Z

← Older revision		Revision as of 16:56, 30 May 2021
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	* [[Nanomechanics is barely mechanical quantummechanics]]		* [[Nanomechanics is barely mechanical quantummechanics]]
	* [[Trapped free particles]]		* [[Trapped free particles]]
			* [[Pages with math]]

			[[Category:Pages with math]]
	[[Category:contains math]]		[[Category:contains math]]

2017-06-21T11:37:32Z

Basics: freedome -> freedom

← Older revision		Revision as of 13:37, 21 June 2017
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	B) sufficiently small mass and moment of inertia. Halving doubles energy quanta.		B) sufficiently small mass and moment of inertia. Halving doubles energy quanta.
	Robotic system = mechanic coupled to a big massive system with only one (controlled) degree of ~~freedome~~ -> energy quanta get to be unmeasurably small.		Robotic system = mechanic coupled to a big massive system with only one (controlled) degree of freedom -> energy quanta get to be unmeasurably small.
	If quantisation is desired: release small part in limited freedom.		If quantisation is desired: release small part in limited freedom.

2016-11-15T19:19:24Z

← Older revision		Revision as of 21:19, 15 November 2016
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	* [[Nanomechanics is barely mechanical quantummechanics]]		* [[Nanomechanics is barely mechanical quantummechanics]]
			* [[Trapped free particles]]

	[[Category:contains math]]		[[Category:contains math]]

2016-11-15T19:02:56Z

added related link

← Older revision		Revision as of 21:02, 15 November 2016
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	<math> \Delta x \Delta p >= h \qquad E = p^2/2m \qquad \Delta E >= h^2 / (2m \cdot \Delta x^2)</math>		<math> \Delta x \Delta p >= h \qquad E = p^2/2m \qquad \Delta E >= h^2 / (2m \cdot \Delta x^2)</math>

			== Related ==

			* [[Nanomechanics is barely mechanical quantummechanics]]

	[[Category:contains math]]		[[Category:contains math]]

2015-04-01T12:48:58Z

← Older revision		Revision as of 14:48, 1 April 2015
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	<math> \Delta x \Delta p >= h \qquad E = p^2/2m \qquad \Delta E >= h^2 / (2m \cdot \Delta x^2)</math>		<math> \Delta x \Delta p >= h \qquad E = p^2/2m \qquad \Delta E >= h^2 / (2m \cdot \Delta x^2)</math>

			[[Category:contains math]]

2015-04-01T12:38:41Z

Quantisation in rotation (angular momentum): = -> >=

← Older revision		Revision as of 14:38, 1 April 2015
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	== Quantisation in rotation (angular momentum) ==		== Quantisation in rotation (angular momentum) ==

	<math> (2 \pi \cdot rad) \Delta L >= h \qquad \Delta L >= h/(2 \pi) = \hbar \qquad E = L^2/(2I) \qquad \Delta E = \hbar^2/(2I)</math>		<math> (2 \pi \cdot rad) \Delta L >= h \qquad \Delta L >= h/(2 \pi) = \hbar \qquad E = L^2/(2I) \qquad \Delta E >= \hbar^2/(2I)</math>

	== Quantisation captured in a box (similar to oszillation) ==		== Quantisation captured in a box (similar to oszillation) ==

	<math> \Delta x \Delta p >= h \qquad E = p^2/2m \qquad \Delta E >= h^2 / (2m \cdot \Delta x^2)</math>		<math> \Delta x \Delta p >= h \qquad E = p^2/2m \qquad \Delta E >= h^2 / (2m \cdot \Delta x^2)</math>

2015-04-01T12:38:21Z

Estimations

← Older revision		Revision as of 14:38, 1 April 2015
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	<math> \langle E_{therm} \rangle =3/2 \cdot k_B T</math>		<math> \langle E_{therm} \rangle =3/2 \cdot k_B T</math>

			Following: zero point energies (need not be equal but are similar in size to quanta)

	== Quantisation in rotation (angular momentum) ==		== Quantisation in rotation (angular momentum) ==

2015-04-01T12:35:40Z

Estimations

← Older revision		Revision as of 14:35, 1 April 2015
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	= Estimations =		= Estimations =

	<math> \langle E_{~~Therm~~} \rangle =3/2 \cdot k_B T</math>		<math> \langle E_{therm} \rangle =3/2 \cdot k_B T</math>

	== Quantisation in rotation (angular momentum) ==		== Quantisation in rotation (angular momentum) ==

2015-04-01T12:35:24Z

Estimations: added expectation value brackets

← Older revision		Revision as of 14:35, 1 April 2015
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	= Estimations =		= Estimations =

	<math>E_{Therm}=3/2 \cdot k_B T</math>		<math> \langle E_{Therm} \rangle =3/2 \cdot k_B T</math>

	== Quantisation in rotation (angular momentum) ==		== Quantisation in rotation (angular momentum) ==