Physics:Quantum mechanics/Timeline - Revision history

WikiHarold: Fix final Quantum red link source

2026-05-24T00:07:48Z

Fix final Quantum red link source

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	Although Heisenberg, Born, and Jordan had already developed a parallel effort using matrices that would prove to be a mathematically equivalent theory<ref>https://en.wikipedia.org/wiki/Quantum_mechanics</ref>), we shall take this as the starting point in our quest for a fully developed theory. While this equation looks intimidating to a novice, it is a standard wave equation that is in many respects simpler than Maxwell's Equations. It is completely deterministic, meaning that it allows one to predict how a wave will evolve (given initial conditions). '''In other words, like Newton's ''<math>F=ma</math>'', equation ('''{{EquationNote\|4}}) '''predicts the future of the wave amplitude''' (We shall soon discover that predicting future values of ψ is not necessarily the same as predicting the future behavior of the particle.)		Although Heisenberg, Born, and Jordan had already developed a parallel effort using matrices that would prove to be a mathematically equivalent theory<ref>https://en.wikipedia.org/wiki/Quantum_mechanics</ref>), we shall take this as the starting point in our quest for a fully developed theory. While this equation looks intimidating to a novice, it is a standard wave equation that is in many respects simpler than Maxwell's Equations. It is completely deterministic, meaning that it allows one to predict how a wave will evolve (given initial conditions). '''In other words, like Newton's ''<math>F=ma</math>'', equation ('''{{EquationNote\|4}}) '''predicts the future of the wave amplitude''' (We shall soon discover that predicting future values of ψ is not necessarily the same as predicting the future behavior of the particle.)

	[[Image:Hydrogen Density Plots.png\|The electron probability density for the first few [[hydrogen atom]] electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.]]		[[Image:Hydrogen Density Plots.png\|The electron probability density for the first few hydrogen atom electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.]]

	To the left are some computer generated solutions Schrödinger's equations for a (very tiny) mass attached to a spring. The symbol, ψ, is spelled psi, but often pronounced "sigh", with a hint of "p" at the beginning. It can also be pronounced "psee". It is called the "wavefunction", and is essentially the "amplitude", analogous to the "height" of the wave. The wavefunctions C through F represent states of known energy not unlike the "allowed" orbits of the Bohr atom. Wavefunctions G and H are more complicated and have no counterpart in Bohr's model of "allowed" states. They are known as "mixed energy" states.		To the left are some computer generated solutions Schrödinger's equations for a (very tiny) mass attached to a spring. The symbol, ψ, is spelled psi, but often pronounced "sigh", with a hint of "p" at the beginning. It can also be pronounced "psee". It is called the "wavefunction", and is essentially the "amplitude", analogous to the "height" of the wave. The wavefunctions C through F represent states of known energy not unlike the "allowed" orbits of the Bohr atom. Wavefunctions G and H are more complicated and have no counterpart in Bohr's model of "allowed" states. They are known as "mixed energy" states.
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	== Quantum cryptography 1984==		== Quantum cryptography 1984==
	[[File:BB84_QKD_protocol_-_Virtual_Lab_by_Quantum_Flytrap.png\|An interactive simulation of an ~~[[Quantum_optics\|~~optical implementation]] of the BB84 quantum key distribution protocol in the Virtual Lab by Quantum Flytrap,<ref>{{cite journal\|last1=Migdał\|first1=Piotr\|last2=Jankiewicz\|first2=Klementyna\|last3=Grabarz\|first3=Paweł\|last4=Decaroli\|first4=Chiara\|last5=Cochin\|first5=Philippe\|title=Visualizing quantum mechanics in an interactive simulation - Virtual Lab by Quantum Flytrap\|journal=Optical Engineering\|volume=61\|issue=8\|article-number=081808\|year=2022\|doi=10.1117/1.OE.61.8.081808\|arxiv=2203.13300}}</ref> [https://lab.quantumflytrap.com/lab/bb84 available online]. In this optical setup, bits are encoded using orthogonal polarization states of photons. Alice and Bob select their measurement bases by rotating the polarization by 0 or 45 degrees using Faraday rotators. Single-photon detectors measure the output after the photons pass through a polarizing beam splitter, which separates the polarizations.]]		[[File:BB84_QKD_protocol_-_Virtual_Lab_by_Quantum_Flytrap.png\|An interactive simulation of an optical implementation of the BB84 quantum key distribution protocol in the Virtual Lab by Quantum Flytrap,<ref>{{cite journal\|last1=Migdał\|first1=Piotr\|last2=Jankiewicz\|first2=Klementyna\|last3=Grabarz\|first3=Paweł\|last4=Decaroli\|first4=Chiara\|last5=Cochin\|first5=Philippe\|title=Visualizing quantum mechanics in an interactive simulation - Virtual Lab by Quantum Flytrap\|journal=Optical Engineering\|volume=61\|issue=8\|article-number=081808\|year=2022\|doi=10.1117/1.OE.61.8.081808\|arxiv=2203.13300}}</ref> [https://lab.quantumflytrap.com/lab/bb84 available online]. In this optical setup, bits are encoded using orthogonal polarization states of photons. Alice and Bob select their measurement bases by rotating the polarization by 0 or 45 degrees using Faraday rotators. Single-photon detectors measure the output after the photons pass through a polarizing beam splitter, which separates the polarizations.]]

	In 1984 Charles Bennett and Gilles Brassard proposed the '''BB84''' protocol.<ref>https://en.wikipedia.org/wiki/BB84</ref> It is the first major protocol for quantum cryptography, especially for quantum key distribution.		In 1984 Charles Bennett and Gilles Brassard proposed the '''BB84''' protocol.<ref>https://en.wikipedia.org/wiki/BB84</ref> It is the first major protocol for quantum cryptography, especially for quantum key distribution.

WikiHarold: Remove final Quantum red link remnants

2026-05-24T00:03:04Z

Remove final Quantum red link remnants

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WikiHarold: Remove imported red links from Quantum page

2026-05-23T23:47:48Z

Remove imported red links from Quantum page

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	and <math>p=mv</math> is momentum. Lambda, or <math>\lambda</math>, is now known as the De Broglie wavelength (although Bohr did not use the De Broglie wavelength to construct this model.) For an electron of mass ,<math>m</math> and velocity <math>v</math>, <math>p=mv</math>.<ref>Incidentally, this equation also holds for photons, where <math>p=h/\lambda</math> is the photon's momentum.</ref>		and <math>p=mv</math> is momentum. Lambda, or <math>\lambda</math>, is now known as the De Broglie wavelength (although Bohr did not use the De Broglie wavelength to construct this model.) For an electron of mass ,<math>m</math> and velocity <math>v</math>, <math>p=mv</math>.<ref>Incidentally, this equation also holds for photons, where <math>p=h/\lambda</math> is the photon's momentum.</ref>

	~~[[Image:Electron_wave_doubling_over.png\|thumb\|left\|430px\|Only the orbit on the left satisfies Bohr's conditions for an "allowed" orbit.]]~~
	[[File:Waves in Box.svg\|thumb\|right\|upright=.75\|These [[Wikipedia:standing waves\|standing waves]] somewhat resemble electrons in the Bohr model. The momentum, and hence the speed and energy of each "orbit" can be calculated from the wavelength.]]		[[File:Waves in Box.svg\|thumb\|right\|upright=.75\|These [[Wikipedia:standing waves\|standing waves]] somewhat resemble electrons in the Bohr model. The momentum, and hence the speed and energy of each "orbit" can be calculated from the wavelength.]]

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	{{reflist\|3}}		{{reflist\|3}}
	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	~~[[Category:Quantum mechanics]]~~
	~~[[Category:Science]]~~
	~~[[Category:History of Physics]]~~

	{{Sourceattribution\|Physics:Quantum mechanics/Timeline\|1}}		{{Sourceattribution\|Physics:Quantum mechanics/Timeline\|1}}

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2026-05-23T22:22:23Z

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	{{Quantum book backlink\|Timeline}}		{{Quantum book backlink\|Timeline}}
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	{{Short description\|Quantum Collection topic on Quantum mechanics/Timeline}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum mechanics/Timeline}}

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	[[File:Quantum_book1_mechanics_timeline_yellow.png\|right\|180px]]This equation predicts that photon energy is directly proportional to frequency; if you double ''f'' then ''E'' doubles. Frequency is inversely proportional to wavelength (since the speed of light is <math>c=f\lambda</math> where λ (lambda) is the length of a wave.		[[File:Quantum_book1_mechanics_timeline_yellow.png\|right\|180px]]This equation predicts that photon energy is directly proportional to frequency; if you double ''f'' then ''E'' doubles. Frequency is inversely proportional to wavelength (since the speed of light is <math>c=f\lambda</math> where λ (lambda) is the length of a wave.


	How Planck constructed his model and performed his calculation is beyond the scope of this essay.		How Planck constructed his model and performed his calculation is beyond the scope of this essay.
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	[[Image:Electron_wave_doubling_over.png\|thumb\|left\|430px\|Only the orbit on the left satisfies Bohr's conditions for an "allowed" orbit.]]		[[Image:Electron_wave_doubling_over.png\|thumb\|left\|430px\|Only the orbit on the left satisfies Bohr's conditions for an "allowed" orbit.]]
	[[File:Waves in Box.svg\|thumb\|right\|upright=.75\|These [[Wikipedia:standing waves\|standing waves]] somewhat resemble electrons in the Bohr model. The momentum, and hence the speed and energy of each "orbit" can be calculated from the wavelength.]]		[[File:Waves in Box.svg\|thumb\|right\|upright=.75\|These [[Wikipedia:standing waves\|standing waves]] somewhat resemble electrons in the Bohr model. The momentum, and hence the speed and energy of each "orbit" can be calculated from the wavelength.]]


	The meaning of allowed orbits can be discerned from the pair of figures situated to the left. The wavelength must be such that the number that fit into a full circumference (2пr) must equal one, or two, or 3, or 4 (and so forth). In one case, the wave fits perfectly in the circles (with exactly four wavelengths). This corresponds to an electron in the third excited state, or n =4. The other wave does not fit into its allowed radius because it doubles over itself. This energy level does not exist for this atom.		The meaning of allowed orbits can be discerned from the pair of figures situated to the left. The wavelength must be such that the number that fit into a full circumference (2пr) must equal one, or two, or 3, or 4 (and so forth). In one case, the wave fits perfectly in the circles (with exactly four wavelengths). This corresponds to an electron in the third excited state, or n =4. The other wave does not fit into its allowed radius because it doubles over itself. This energy level does not exist for this atom.
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	<math>\omega=2\pi f</math> is the angular frequency. In these variables, we have		<math>\omega=2\pi f</math> is the angular frequency. In these variables, we have
	<math> p = mv = \hbar k </math>, and <math>E = \hbar \omega</math>.		<math> p = mv = \hbar k </math>, and <math>E = \hbar \omega</math>.


	Although we are using the de Broglie relations within the context of the non-relativistic quantum theory, much of de Broglie's argument was based on Einstein's theory of special relativity, which describes how length, time, mass and energy are perceived by observers who are moving relative to one another. The figure on the left shows the crests and troughs of a travelling wave (in blue and red). Einstein's special theory of relativity inertial reference frames describes how different observers (moving at different speeds) will perceive length, time, speed, momentum, and energy. Self-consistency is possible only if frequency-wavenumber is proportional to energy-momentum. Mathematically, De Broglie derived only the need for this proportionality, not its value. But it was clear that ''<big>ħ</big>'' is that constant.		Although we are using the de Broglie relations within the context of the non-relativistic quantum theory, much of de Broglie's argument was based on Einstein's theory of special relativity, which describes how length, time, mass and energy are perceived by observers who are moving relative to one another. The figure on the left shows the crests and troughs of a travelling wave (in blue and red). Einstein's special theory of relativity inertial reference frames describes how different observers (moving at different speeds) will perceive length, time, speed, momentum, and energy. Self-consistency is possible only if frequency-wavenumber is proportional to energy-momentum. Mathematically, De Broglie derived only the need for this proportionality, not its value. But it was clear that ''<big>ħ</big>'' is that constant.
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	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	~~==See also==~~
	==Physics:Quantum_mechanics/Timeline/Quiz/==		==Physics:Quantum_mechanics/Timeline/Quiz/==
	See the subpage for a quiz on this topic.		See the subpage for a quiz on this topic.