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Deriving the Bloch's theorem
Bloch’s theorem is a general statement about the shape and symmetry of the wavefunction of electrons in a periodic potential, such as in crystalline solids. Bloch’s theorem unravels the subtleties of the electronic behavior in solids, such as why electrons can travel large distances in a crystal lattice, much longer than interatomic spacing, without scattering. In this video, we’re going to go through the basics of Bloch’s theorem, explaining why it is the case and its implications to the behavior of electrons in crystalline materials. We will begin by discussing the topic of spatially periodic potentials and periodic boundary conditions for the wave function of electrons. Next, we’re going to state Bloch’s theorem and prove it by directly solving the time-independent Schrodinger equation ...
published: 05 Nov 2022
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14 - Bloch waves
A very short introduction of Bloch waves in TEM
published: 30 Oct 2019
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Bloch's Theorem in Crystals
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
In this video I sketch out a basic proof of Bloch's theorem in crystals and also talk about where it breaks down and why we might want to use it.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.
published: 29 May 2019
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Measuring Bloch Waves | Research in 60 Seconds
Electrons behave differently in materials than they do in free space, and understanding how is critical for scientists studying material properties and engineers looking to develop new technologies. The movement of electrons through solids is called their Bloch Wave function. Researchers in Professor Mark Sherwin’s lab are using UC Santa Barbara’s free-electron laser to experimentally reconstruct these wavefunctions for the first time.
Professor Sherwin and his research group explain their groundbreaking research in just a minute,
As an elite research university, UC Santa Barbara is home to world-renowned faculty across the disciplines — from the hard sciences, to the social sciences, to the humanities and the arts. These esteemed scholars and scientists are conducting their research n...
published: 17 May 2022
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Lecture -- Electromagnetic Waves in Periodic Structures
This lecture discusses electromagnetic waves propagating inside of periodic structures. Topics include Bloch's theorem, band diagrams, isofrequency contours, and some examples.
published: 16 May 2020
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Hans Bethe - Felix Bloch's theory of conduction in metals (17/158)
To hear more of Hans Bethe’s stories, go to the playlist: https://www.youtube.com/watch?v=LvgLyzTEmJk&list=PLVV0r6CmEsFyUDSroBQVEcbnNud7I9xom
German-born theoretical physicist Hans Bethe (1906-2005) was one of the first scientists to join the Manhattan Project, later strongly advocating nuclear disarmament. In 1967, he was awarded the Nobel Prize in Physics for his theory of stellar nucleosynthesis. [Listener: Sam Schweber; date recorded: 1996]
TRANSCRIPT: The electron wave in a solid has the periodicity of the crystal, and... but it... you can have an electron propagating freely in the solid. That was very much in Sommerfeld's mind too, and it then became the basis of Bloch's theory of conduction in metals, where you had wave functions which had... were like free wave functions but modu...
published: 27 Jun 2017
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Bloch theorem derivation – David Miller
See https://web.stanford.edu/group/dabmgroup/cgi-bin/dabm/teaching/quantum-mechanics/ for links to all videos, slides, FAQs, and complete open online quantum classes.
Lecture 28b of Quantum Mechanics for Scientists and Engineers
Part of Lecture 28 The Bloch theorem
Text reference: Section 8.3 (from Eq. 8.7), QMSE
QMSE - D. A. B. Miller, Quantum Mechanics for Scientists and Engineers (Cambridge)
published: 13 Dec 2021
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PWEM-2D Full Band Calculation and Visualization of Bloch Modes
This video animates the construction of a photonic band diagram for a 2D lattice. At the upper left is a depiction of a 3x3 section of the lattice. At the lower left is the Brillouin zone, irreducible Brillouin zone (IBZ), and the current Bloch wave vector for each iteration of the calculation. The center diagram shows the full photonic band diagram as the eigen-values are added after simulating the current Bloch wave vector. At right are two diagrams showing the Bloch mode for the first two bands at each Bloch wave vector.
published: 28 Jul 2017
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Bloch wave
Bloch wave
published: 15 Dec 2012
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Bloch's Theorem and Fourier Series
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
There is a deep connection between Bloch's Theorem and the Fourier Series/Transform representation. In this video, I show how you can derive the Fourier Series from continuous symmetry in space, while Bloch's Theorem used discrete symmetry.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anyt...
published: 30 May 2019
11:43
Deriving the Bloch's theorem
Bloch’s theorem is a general statement about the shape and symmetry of the wavefunction of electrons in a periodic potential, such as in crystalline solids. Blo...
Bloch’s theorem is a general statement about the shape and symmetry of the wavefunction of electrons in a periodic potential, such as in crystalline solids. Bloch’s theorem unravels the subtleties of the electronic behavior in solids, such as why electrons can travel large distances in a crystal lattice, much longer than interatomic spacing, without scattering. In this video, we’re going to go through the basics of Bloch’s theorem, explaining why it is the case and its implications to the behavior of electrons in crystalline materials. We will begin by discussing the topic of spatially periodic potentials and periodic boundary conditions for the wave function of electrons. Next, we’re going to state Bloch’s theorem and prove it by directly solving the time-independent Schrodinger equation in a periodic potential.
Technical Content: Duarte Sousa, Tony Low
Video Production: Katie Low, Tony Low
Erratum
9:25: k is only defined modulo G, thus we can arbitrary shift k by +-G. The step to obtaining the matrix form uses this fact.
https://wn.com/Deriving_The_Bloch's_Theorem
Bloch’s theorem is a general statement about the shape and symmetry of the wavefunction of electrons in a periodic potential, such as in crystalline solids. Bloch’s theorem unravels the subtleties of the electronic behavior in solids, such as why electrons can travel large distances in a crystal lattice, much longer than interatomic spacing, without scattering. In this video, we’re going to go through the basics of Bloch’s theorem, explaining why it is the case and its implications to the behavior of electrons in crystalline materials. We will begin by discussing the topic of spatially periodic potentials and periodic boundary conditions for the wave function of electrons. Next, we’re going to state Bloch’s theorem and prove it by directly solving the time-independent Schrodinger equation in a periodic potential.
Technical Content: Duarte Sousa, Tony Low
Video Production: Katie Low, Tony Low
Erratum
9:25: k is only defined modulo G, thus we can arbitrary shift k by +-G. The step to obtaining the matrix form uses this fact.
- published: 05 Nov 2022
- views: 16700
5:36
14 - Bloch waves
A very short introduction of Bloch waves in TEM
A very short introduction of Bloch waves in TEM
https://wn.com/14_Bloch_Waves
A very short introduction of Bloch waves in TEM
- published: 30 Oct 2019
- views: 5193
13:01
Bloch's Theorem in Crystals
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming ...
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
In this video I sketch out a basic proof of Bloch's theorem in crystals and also talk about where it breaks down and why we might want to use it.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.
https://wn.com/Bloch's_Theorem_In_Crystals
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
In this video I sketch out a basic proof of Bloch's theorem in crystals and also talk about where it breaks down and why we might want to use it.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.
- published: 29 May 2019
- views: 70339
1:14
Measuring Bloch Waves | Research in 60 Seconds
Electrons behave differently in materials than they do in free space, and understanding how is critical for scientists studying material properties and engineer...
Electrons behave differently in materials than they do in free space, and understanding how is critical for scientists studying material properties and engineers looking to develop new technologies. The movement of electrons through solids is called their Bloch Wave function. Researchers in Professor Mark Sherwin’s lab are using UC Santa Barbara’s free-electron laser to experimentally reconstruct these wavefunctions for the first time.
Professor Sherwin and his research group explain their groundbreaking research in just a minute,
As an elite research university, UC Santa Barbara is home to world-renowned faculty across the disciplines — from the hard sciences, to the social sciences, to the humanities and the arts. These esteemed scholars and scientists are conducting their research not only on campus, but all over the world. The award-winning video series "Research in 60 Seconds" highlights some of their pioneering advances and brilliant discoveries, in just about a minute. Watch the short yet engaging and informative segments housed here to learn more about the fascinating work coming out of UC Santa Barbara.
#UCSantaBarbara #UCSB #Researchin60
https://wn.com/Measuring_Bloch_Waves_|_Research_In_60_Seconds
Electrons behave differently in materials than they do in free space, and understanding how is critical for scientists studying material properties and engineers looking to develop new technologies. The movement of electrons through solids is called their Bloch Wave function. Researchers in Professor Mark Sherwin’s lab are using UC Santa Barbara’s free-electron laser to experimentally reconstruct these wavefunctions for the first time.
Professor Sherwin and his research group explain their groundbreaking research in just a minute,
As an elite research university, UC Santa Barbara is home to world-renowned faculty across the disciplines — from the hard sciences, to the social sciences, to the humanities and the arts. These esteemed scholars and scientists are conducting their research not only on campus, but all over the world. The award-winning video series "Research in 60 Seconds" highlights some of their pioneering advances and brilliant discoveries, in just about a minute. Watch the short yet engaging and informative segments housed here to learn more about the fascinating work coming out of UC Santa Barbara.
#UCSantaBarbara #UCSB #Researchin60
- published: 17 May 2022
- views: 920
28:37
Lecture -- Electromagnetic Waves in Periodic Structures
This lecture discusses electromagnetic waves propagating inside of periodic structures. Topics include Bloch's theorem, band diagrams, isofrequency contours, a...
This lecture discusses electromagnetic waves propagating inside of periodic structures. Topics include Bloch's theorem, band diagrams, isofrequency contours, and some examples.
https://wn.com/Lecture_Electromagnetic_Waves_In_Periodic_Structures
This lecture discusses electromagnetic waves propagating inside of periodic structures. Topics include Bloch's theorem, band diagrams, isofrequency contours, and some examples.
- published: 16 May 2020
- views: 14412
1:58
Hans Bethe - Felix Bloch's theory of conduction in metals (17/158)
To hear more of Hans Bethe’s stories, go to the playlist: https://www.youtube.com/watch?v=LvgLyzTEmJk&list=PLVV0r6CmEsFyUDSroBQVEcbnNud7I9xom
German-born theor...
To hear more of Hans Bethe’s stories, go to the playlist: https://www.youtube.com/watch?v=LvgLyzTEmJk&list=PLVV0r6CmEsFyUDSroBQVEcbnNud7I9xom
German-born theoretical physicist Hans Bethe (1906-2005) was one of the first scientists to join the Manhattan Project, later strongly advocating nuclear disarmament. In 1967, he was awarded the Nobel Prize in Physics for his theory of stellar nucleosynthesis. [Listener: Sam Schweber; date recorded: 1996]
TRANSCRIPT: The electron wave in a solid has the periodicity of the crystal, and... but it... you can have an electron propagating freely in the solid. That was very much in Sommerfeld's mind too, and it then became the basis of Bloch's theory of conduction in metals, where you had wave functions which had... were like free wave functions but modulated with the periodicity of the crystal. That was the basis of... of the theory of conductivity and it was also used by Brillouin and then by Peierls in talking about finer details of the behavior of electron wave functions in a crystal.
[SS] Then you master all of these...
All of these were familiar to me. I wasn't clever enough to do Bloch's theory of... of conduction in... in metals, but later on in... in Handbuch article with Sommerfeld I discussed all these.
https://wn.com/Hans_Bethe_Felix_Bloch's_Theory_Of_Conduction_In_Metals_(17_158)
To hear more of Hans Bethe’s stories, go to the playlist: https://www.youtube.com/watch?v=LvgLyzTEmJk&list=PLVV0r6CmEsFyUDSroBQVEcbnNud7I9xom
German-born theoretical physicist Hans Bethe (1906-2005) was one of the first scientists to join the Manhattan Project, later strongly advocating nuclear disarmament. In 1967, he was awarded the Nobel Prize in Physics for his theory of stellar nucleosynthesis. [Listener: Sam Schweber; date recorded: 1996]
TRANSCRIPT: The electron wave in a solid has the periodicity of the crystal, and... but it... you can have an electron propagating freely in the solid. That was very much in Sommerfeld's mind too, and it then became the basis of Bloch's theory of conduction in metals, where you had wave functions which had... were like free wave functions but modulated with the periodicity of the crystal. That was the basis of... of the theory of conductivity and it was also used by Brillouin and then by Peierls in talking about finer details of the behavior of electron wave functions in a crystal.
[SS] Then you master all of these...
All of these were familiar to me. I wasn't clever enough to do Bloch's theory of... of conduction in... in metals, but later on in... in Handbuch article with Sommerfeld I discussed all these.
- published: 27 Jun 2017
- views: 4753
17:26
Bloch theorem derivation – David Miller
See https://web.stanford.edu/group/dabmgroup/cgi-bin/dabm/teaching/quantum-mechanics/ for links to all videos, slides, FAQs, and complete open online quantum cl...
See https://web.stanford.edu/group/dabmgroup/cgi-bin/dabm/teaching/quantum-mechanics/ for links to all videos, slides, FAQs, and complete open online quantum classes.
Lecture 28b of Quantum Mechanics for Scientists and Engineers
Part of Lecture 28 The Bloch theorem
Text reference: Section 8.3 (from Eq. 8.7), QMSE
QMSE - D. A. B. Miller, Quantum Mechanics for Scientists and Engineers (Cambridge)
https://wn.com/Bloch_Theorem_Derivation_–_David_Miller
See https://web.stanford.edu/group/dabmgroup/cgi-bin/dabm/teaching/quantum-mechanics/ for links to all videos, slides, FAQs, and complete open online quantum classes.
Lecture 28b of Quantum Mechanics for Scientists and Engineers
Part of Lecture 28 The Bloch theorem
Text reference: Section 8.3 (from Eq. 8.7), QMSE
QMSE - D. A. B. Miller, Quantum Mechanics for Scientists and Engineers (Cambridge)
- published: 13 Dec 2021
- views: 1819
0:33
PWEM-2D Full Band Calculation and Visualization of Bloch Modes
This video animates the construction of a photonic band diagram for a 2D lattice. At the upper left is a depiction of a 3x3 section of the lattice. At the low...
This video animates the construction of a photonic band diagram for a 2D lattice. At the upper left is a depiction of a 3x3 section of the lattice. At the lower left is the Brillouin zone, irreducible Brillouin zone (IBZ), and the current Bloch wave vector for each iteration of the calculation. The center diagram shows the full photonic band diagram as the eigen-values are added after simulating the current Bloch wave vector. At right are two diagrams showing the Bloch mode for the first two bands at each Bloch wave vector.
https://wn.com/Pwem_2D_Full_Band_Calculation_And_Visualization_Of_Bloch_Modes
This video animates the construction of a photonic band diagram for a 2D lattice. At the upper left is a depiction of a 3x3 section of the lattice. At the lower left is the Brillouin zone, irreducible Brillouin zone (IBZ), and the current Bloch wave vector for each iteration of the calculation. The center diagram shows the full photonic band diagram as the eigen-values are added after simulating the current Bloch wave vector. At right are two diagrams showing the Bloch mode for the first two bands at each Bloch wave vector.
- published: 28 Jul 2017
- views: 6839
10:49
Bloch's Theorem and Fourier Series
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming ...
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
There is a deep connection between Bloch's Theorem and the Fourier Series/Transform representation. In this video, I show how you can derive the Fourier Series from continuous symmetry in space, while Bloch's Theorem used discrete symmetry.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.
https://wn.com/Bloch's_Theorem_And_Fourier_Series
https://www.patreon.com/edmundsj
If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible.
There is a deep connection between Bloch's Theorem and the Fourier Series/Transform representation. In this video, I show how you can derive the Fourier Series from continuous symmetry in space, while Bloch's Theorem used discrete symmetry.
This is part of my graduate series on optoelectronics / photonics, and is based primarily on Coldren's book on Lasers as well as graduate-level coursework I have taken in the EECS department at UC Berkeley.
Hope you found this video helpful, please post in the comments below anything I can do to improve future videos, or suggestions you have for future videos.
- published: 30 May 2019
- views: 19807
Chicago Tribune
23 Aug 2024
Chicago Tribune
23 Aug 2024