User:Tohline/Appendix/CGH/QuantumTransitions - Revision history

Tohline: /* Second Thoughts */

2019-05-26T01:54:46Z

Second Thoughts

← Older revision		Revision as of 01:54, 26 May 2019
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	So, assuming that the hologram — e.g., apertures cut out of a thin spherical shell — is stationary, the incoming photon that strikes the hologram will be represented by a certain well-defined, traveling wave packet and, if ionization is successfully achieved, the outgoing electron will be represented by a different (but, still, a certain well-defined) traveling wave packet.		So, assuming that the hologram — e.g., apertures cut out of a thin spherical shell — is stationary, the incoming photon that strikes the hologram will be represented by a certain well-defined, traveling wave packet and, if ionization is successfully achieved, the outgoing electron will be represented by a different (but, still, a certain well-defined) traveling wave packet.

	A subsection of a wikipedia article titled, ''[https://en.wikipedia.org/wiki/Hydrogen_atom#Visualizing_the_hydrogen_electron_orbitals Visualizing the hydrogen electron orbitals]'', displays a cross-sectional image of the probability distributions of ~~nine~~ separate electron orbitals.		A subsection of a wikipedia article titled, ''[https://en.wikipedia.org/wiki/Hydrogen_atom#Visualizing_the_hydrogen_electron_orbitals Visualizing the hydrogen electron orbitals]'', displays a cross-sectional image of the probability distributions of six separate electron orbitals.

	==Characteristic Size and Spin==		==Characteristic Size and Spin==

Tohline: /* Second Thoughts */

2019-05-26T01:53:59Z

Second Thoughts

← Older revision		Revision as of 01:53, 26 May 2019
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	So, assuming that the hologram — e.g., apertures cut out of a thin spherical shell — is stationary, the incoming photon that strikes the hologram will be represented by a certain well-defined, traveling wave packet and, if ionization is successfully achieved, the outgoing electron will be represented by a different (but, still, a certain well-defined) traveling wave packet.		So, assuming that the hologram — e.g., apertures cut out of a thin spherical shell — is stationary, the incoming photon that strikes the hologram will be represented by a certain well-defined, traveling wave packet and, if ionization is successfully achieved, the outgoing electron will be represented by a different (but, still, a certain well-defined) traveling wave packet.

			A subsection of a wikipedia article titled, ''[https://en.wikipedia.org/wiki/Hydrogen_atom#Visualizing_the_hydrogen_electron_orbitals Visualizing the hydrogen electron orbitals]'', displays a cross-sectional image of the probability distributions of nine separate electron orbitals.

	==Characteristic Size and Spin==		==Characteristic Size and Spin==

Tohline: /* Second Thoughts */

2019-05-26T01:25:33Z

Second Thoughts

← Older revision		Revision as of 01:25, 26 May 2019
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	===Second Thoughts===		===Second Thoughts===

	Keep in mind that a free electron or a free photon is represented by a ''wave packet'' — see [https://en.wikipedia.org/wiki/Wave_packet Wikipedia's graphical illustration]. "Depending on the wave equation, the wave packet's profile may remain constant (no dispersion) or it may change (dispersion) while propagating.		Keep in mind that a free electron or a free photon is represented by a ''wave packet'' — see [https://en.wikipedia.org/wiki/Wave_packet Wikipedia's graphical illustration]. "Depending on the wave equation, the wave packet's profile may remain constant (no dispersion) or it may change (dispersion) while propagating."

			So, assuming that the hologram — e.g., apertures cut out of a thin spherical shell — is stationary, the incoming photon that strikes the hologram will be represented by a certain well-defined, traveling wave packet and, if ionization is successfully achieved, the outgoing electron will be represented by a different (but, still, a certain well-defined) traveling wave packet.

	==Characteristic Size and Spin==		==Characteristic Size and Spin==

Tohline: /* Speculation Regarding Quantum Transitions */

2019-05-25T20:19:15Z

Speculation Regarding Quantum Transitions

← Older revision		Revision as of 20:19, 25 May 2019
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	===Second Thoughts===		===Second Thoughts===

			Keep in mind that a free electron or a free photon is represented by a ''wave packet'' — see [https://en.wikipedia.org/wiki/Wave_packet Wikipedia's graphical illustration]. "Depending on the wave equation, the wave packet's profile may remain constant (no dispersion) or it may change (dispersion) while propagating.

Tohline at 20:07, 14 April 2019

2019-04-14T20:07:37Z

← Older revision		Revision as of 20:07, 14 April 2019
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	=See Also=		=See Also=
	* ~~Tohline, J. E., (2008) Computing in Science & Engineering, vol. 10, no. 4~~, ~~pp. 84-85 —~~ ''~~Where is My Digital Holographic Display?'' [ [http://www.phys.lsu.edu/~tohline/CiSE/CiSE2008.Vol10No4.pdf PDF] ]~~
	* [https://~~en.wikipedia.org/wiki/Diffraction Diffraction] (Wikipedia)~~		* Page 56 of the April 2019 issue of Physics Today contains a brief review of the recently published book titled, ''[https://mitpress.mit.edu/books/holographic-quantum-matter Holographic Quantum Matter]'', by Sean A. Hartnoll, Andrew Lucas, & Subir Sachdev (MIT Press); see also the available [https://arxiv.org/pdf/1612.07324.pdf PDF-formatted arXiv] version.
	* Various Google hits:
	** [http://labman.phys.~~utk~~.edu/~~phys222core~~/~~modules/m9/diffraction.htm Single Slit Diffraction~~] ~~(University of Tennessee~~, ~~Knoxville)~~
	** [http://www.~~animations.physics.unsw.edu.au/jw/light/single-slit-diffraction.html Diffraction from a Single Slit~~; ~~Young's Experiment with Finite Slits]~~ (~~University of New South Wales, Sydney, Australia~~)
	** [~~http~~://~~www~~.~~math~~.~~ubc~~.~~ca/~cass/courses/m309-03a/m309~~-~~projects/krzak/ Single Slit Diffraction Pattern of Light~~] ~~(University of British Columbia, Canada)~~
	** [http://hyperphysics.phy-astr.gsu.~~edu/hbase/phyopt/sinslit.html Fraunhofer Single Slit] (Georgia State University)~~
	* [https://en.wikipedia.org/wiki/Hydrogen_atom Hydrogen Atom] (Wikipedia)		* [https://en.wikipedia.org/wiki/Hydrogen_atom Hydrogen Atom] (Wikipedia)


	{{LSU_HBook_footer}}		{{LSU_HBook_footer}}

Tohline: /* Speculation Regarding Quantum Transitions */

2019-04-10T19:28:14Z

Speculation Regarding Quantum Transitions

← Older revision		Revision as of 19:28, 10 April 2019
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	==Quantum Wavefunction==		==Quantum Wavefunction==
			===First Thoughts===

	This sounds suspiciously like photoemission or an atomic transition:		This sounds suspiciously like photoemission or an atomic transition:
	<ol type="A">		<ol type="A">
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	Also, it "explains" why the atomic state cannot be measured without necessarily altering the state.		Also, it "explains" why the atomic state cannot be measured without necessarily altering the state.

			===Second Thoughts===


	==Characteristic Size and Spin==		==Characteristic Size and Spin==

Tohline: /* Characteristic Size and Spin */

2019-04-06T03:22:43Z

Characteristic Size and Spin

← Older revision		Revision as of 03:22, 6 April 2019
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	</table>		</table>

	What is the spin period if we set this angular momentum to half of the Planck constant?		What is the spin period if we set this angular momentum to ''half'' of the Planck constant?
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

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	</td>		</td>
	<td align="left">		<td align="left">
	<math>~\frac{4\pi}{3}\cdot \frac{m_e a_0^2}{\hbar} = 1.6 \times 10^{-17}~\mathrm{s} \, .</math>		<math>~\frac{8\pi}{3}\cdot \frac{m_e a_0^2}{\hbar} = 3.2 \times 10^{-17}~\mathrm{s} \, .</math>
	</td>		</td>
	</tr>		</tr>
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	</td>		</td>
	<td align="left">		<td align="left">
	<math>~46 \, .</math>		<math>~92 \, .</math>
	</td>		</td>
	</tr>		</tr>

Tohline: /* Characteristic Size and Spin */

2019-04-06T03:02:55Z

Characteristic Size and Spin

← Older revision		Revision as of 03:02, 6 April 2019
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	For comparison, what is the light-travel time across the sphere?		For comparison, what is the light-travel time across the sphere?
	<~~div~~ align="center"><math>~t = \frac{~~a_0~~}{c} = 1.76 \times 10^{-19} ~\mathrm{s}\, .</math></~~div~~>
			<table border="0" cellpadding="5" align="center">

			<tr>
			<td align="right">
			<math>~t</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~\frac{2a_0}{c} = 3.5 \times 10^{-19} ~\mathrm{s}</math>
			</td>
			</tr>

			<tr>
			<td align="right">
			<math>~\Rightarrow ~~~ \frac{P}{t}</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~46 \, .</math>
			</td>
			</tr>
			</table>

	=See Also=		=See Also=

Tohline: /* Characteristic Size and Spin */

2019-04-06T02:55:51Z

Characteristic Size and Spin

← Older revision		Revision as of 02:55, 6 April 2019
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	</td>		</td>
	<td align="left">		<td align="left">
	<math>~\frac{4\pi}{3}\cdot \frac{m_e a_0^2}{\hbar} = 3.2 \times 10^{-57}~\mathrm{s} \, .</math>		<math>~\frac{4\pi}{3}\cdot \frac{m_e a_0^2}{\hbar} = 1.6 \times 10^{-17}~\mathrm{s} \, .</math>
	</td>		</td>
	</tr>		</tr>

Tohline: /* Characteristic Size and Spin */

2019-04-06T02:53:50Z

Characteristic Size and Spin

← Older revision		Revision as of 02:53, 6 April 2019
Line 35:		Line 35:
	==Characteristic Size and Spin==		==Characteristic Size and Spin==

	What is the angular momentum of a spherical shell spinning with angular frequency, <math>~omega</math>, whose radius is the Bohr radius and whose mass is one electron mass? Compare this to <math>~\hbar</math>.		What is the angular momentum of a spherical shell spinning with angular frequency, <math>~\omega</math>, whose radius is the Bohr radius <math>~(a_0 = 5.29 \times 10^{-11}~\mathrm{m})</math> and whose mass is one electron mass <math>~(m_e = 9.1\times 10^{-31} ~\mathrm{kg})</math>? Compare this to <math>~\hbar = 6.6 \times 10^{-34}~\mathrm{kg} \cdot \mathrm{m}^2/\mathrm{s}</math>. Drawing from [https://en.wikipedia.org/wiki/List_of_moments_of_inertia Wikipedia], the relevant moment of inertia is,
			<table border="0" cellpadding="5" align="center">

			<tr>
			<td align="right">
			<math>~I</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~\frac{2}{3} m_e a_0^2 </math>
			</td>
			</tr>

			<tr>
			<td align="right">
			<math>~\Rightarrow ~~~L</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~\frac{2}{3} m_e a_0^2 \omega \, .</math>
			</td>
			</tr>
			</table>

			What is the spin period if we set this angular momentum to half of the Planck constant?
			<table border="0" cellpadding="5" align="center">

			<tr>
			<td align="right">
			<math>~P = \frac{2\pi}{\omega}</math>
			</td>
			<td align="center">
			<math>~=</math>
			</td>
			<td align="left">
			<math>~\frac{4\pi}{3}\cdot \frac{m_e a_0^2}{\hbar} = 3.2 \times 10^{-57}~\mathrm{s} \, .</math>
			</td>
			</tr>
			</table>

			For comparison, what is the light-travel time across the sphere?
			<div align="center"><math>~t = \frac{a_0}{c} = 1.76 \times 10^{-19} ~\mathrm{s}\, .</math></div>

	=See Also=		=See Also=