No Cloning Theorem with essential Mathematics and PhysicsRitajit Majumdar
This is the first project report at my University. This report describes No Cloning Theorem, an introductory topic of Quantum Computation and Quantum Information Theory. The report also covers the necessary mathematics and physics.
Magnetism is a force that can attract or repel magnetic materials like iron. It is a property of substances that are attracted to magnets. There are different types of magnetism including permanent magnetism, temporary magnetism caused by magnetic fields, and electromagnetism related to electric currents and changing magnetic fields. Magnets have north and south poles and attract unlike poles while repelling like poles. The strength of magnetic force depends on the strength of the magnets and the distance between them.
Chapter3 introduction to the quantum theory of solidsK. M.
The document provides an introduction to the quantum theory of solids, including:
1. How allowed and forbidden energy bands form in solids due to the interaction of atomic electron wave functions when atoms are brought close together in a crystal lattice.
2. Electrical conduction in solids is explained using the concept of electron effective mass and holes, within the framework of the energy band model.
3. The Kronig-Penney model is used to quantitatively relate the energy, wave number, and periodic potential within a solid, resulting in allowed and forbidden energy bands.
CH2 MQ : EVOLUTION D’UNE PARTICULE QUANTIQUE LIBREAliBenMoussa10
Diapos du cours du deuxième chapitre de Mécanique quantique pour les étudiants des classes préparatoires aux concours nationaux d'entrée aux cycles de formation d'ingénieurs - Tunisie
The document discusses the Bethe-Salpeter equation (BSE) which accounts for electron-hole interactions beyond the independent particle approximation. It summarizes that the BSE is derived from the equation of motion for the response function and results in an effective two-particle Hamiltonian that describes electron-hole excitations when diagonalized. Solving the BSE for lithium fluoride improves agreement with experimental optical spectra by including excitonic effects neglected by the independent particle picture.
La maintenance est un ensemble des actions permettant de maintenir ou de rétablir un bien dans un état spécifié ou en mesure d’assurer un service déterminé. Bien maintenir, c’est assurer ces opérations au coût optimal.
Publikacja zawiera najlepsze (w mojej ocenie) wpisy, które pojawiły się na moim blogu 2minuty.pl.
Ebook jest darmowy.
Patronat wydania: wydawnictwo EscapeMagazine.pl, http://www.EscapeMagazine.pl
1) The document describes a canonical transformation from the original (x, p) coordinates to new canonical coordinates (X, P) for the harmonic oscillator Hamiltonian.
2) An explicit transformation is found using a generating function of type 1. The new coordinates (X, P) correspond to an action-angle pair where P is the action (energy) and X is the cyclic coordinate proportional to time.
3) In the new coordinates, the Hamiltonian and equations of motion simplify greatly, with P being a constant of motion and X varying linearly with time.
This presentation discusses using transformation optics and finite-difference time-domain (FDTD) simulations to design metamaterials that manipulate light in desired ways. It begins with an overview of transformation optics and how material parameters can be derived to effect a spatial transformation on light rays. An example of a "beam turner" is presented, along with the calculations to determine the required inhomogeneous, bi-anisotropic material properties. The presentation then discusses using FDTD simulations to model light propagation through these designed materials by discretizing Maxwell's equations in space and time. Examples shown include simulations of the beam turner and cloaking devices.
The WKB approximation is a method to find approximate solutions to the Schrodinger equation. It was developed in 1926 by Wentzel, Kramer, and Brillouin. The approximation assumes the wavefunction is an exponentially varying function with amplitude and phase that change slowly compared to the de Broglie wavelength. It can be used to obtain approximate solutions and energy eigenvalues for systems where the classical limit is valid. The approximation breaks down near classical turning points where the particle's energy is equal to the potential energy. The document provides examples of using the WKB approximation to solve the time-independent Schrodinger equation in one dimension for cases where the particle's energy is both greater than and less than the potential energy.
This document discusses statistical mechanics and the distribution of energy among particles in a system. It provides 3 main types of statistical distributions based on the properties of identical particles: Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics. Maxwell-Boltzmann statistics applies to distinguishable particles, while Bose-Einstein and Fermi-Dirac apply to indistinguishable particles (bosons and fermions respectively), with the key difference being that fermions obey the Pauli exclusion principle. The document also discusses applications of these distributions, including the Maxwell-Boltzmann distribution law for molecular energies in an ideal gas.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
No Cloning Theorem with essential Mathematics and PhysicsRitajit Majumdar
This is the first project report at my University. This report describes No Cloning Theorem, an introductory topic of Quantum Computation and Quantum Information Theory. The report also covers the necessary mathematics and physics.
Magnetism is a force that can attract or repel magnetic materials like iron. It is a property of substances that are attracted to magnets. There are different types of magnetism including permanent magnetism, temporary magnetism caused by magnetic fields, and electromagnetism related to electric currents and changing magnetic fields. Magnets have north and south poles and attract unlike poles while repelling like poles. The strength of magnetic force depends on the strength of the magnets and the distance between them.
Chapter3 introduction to the quantum theory of solidsK. M.
The document provides an introduction to the quantum theory of solids, including:
1. How allowed and forbidden energy bands form in solids due to the interaction of atomic electron wave functions when atoms are brought close together in a crystal lattice.
2. Electrical conduction in solids is explained using the concept of electron effective mass and holes, within the framework of the energy band model.
3. The Kronig-Penney model is used to quantitatively relate the energy, wave number, and periodic potential within a solid, resulting in allowed and forbidden energy bands.
CH2 MQ : EVOLUTION D’UNE PARTICULE QUANTIQUE LIBREAliBenMoussa10
Diapos du cours du deuxième chapitre de Mécanique quantique pour les étudiants des classes préparatoires aux concours nationaux d'entrée aux cycles de formation d'ingénieurs - Tunisie
The document discusses the Bethe-Salpeter equation (BSE) which accounts for electron-hole interactions beyond the independent particle approximation. It summarizes that the BSE is derived from the equation of motion for the response function and results in an effective two-particle Hamiltonian that describes electron-hole excitations when diagonalized. Solving the BSE for lithium fluoride improves agreement with experimental optical spectra by including excitonic effects neglected by the independent particle picture.
La maintenance est un ensemble des actions permettant de maintenir ou de rétablir un bien dans un état spécifié ou en mesure d’assurer un service déterminé. Bien maintenir, c’est assurer ces opérations au coût optimal.
Publikacja zawiera najlepsze (w mojej ocenie) wpisy, które pojawiły się na moim blogu 2minuty.pl.
Ebook jest darmowy.
Patronat wydania: wydawnictwo EscapeMagazine.pl, http://www.EscapeMagazine.pl
1) The document describes a canonical transformation from the original (x, p) coordinates to new canonical coordinates (X, P) for the harmonic oscillator Hamiltonian.
2) An explicit transformation is found using a generating function of type 1. The new coordinates (X, P) correspond to an action-angle pair where P is the action (energy) and X is the cyclic coordinate proportional to time.
3) In the new coordinates, the Hamiltonian and equations of motion simplify greatly, with P being a constant of motion and X varying linearly with time.
This presentation discusses using transformation optics and finite-difference time-domain (FDTD) simulations to design metamaterials that manipulate light in desired ways. It begins with an overview of transformation optics and how material parameters can be derived to effect a spatial transformation on light rays. An example of a "beam turner" is presented, along with the calculations to determine the required inhomogeneous, bi-anisotropic material properties. The presentation then discusses using FDTD simulations to model light propagation through these designed materials by discretizing Maxwell's equations in space and time. Examples shown include simulations of the beam turner and cloaking devices.
The WKB approximation is a method to find approximate solutions to the Schrodinger equation. It was developed in 1926 by Wentzel, Kramer, and Brillouin. The approximation assumes the wavefunction is an exponentially varying function with amplitude and phase that change slowly compared to the de Broglie wavelength. It can be used to obtain approximate solutions and energy eigenvalues for systems where the classical limit is valid. The approximation breaks down near classical turning points where the particle's energy is equal to the potential energy. The document provides examples of using the WKB approximation to solve the time-independent Schrodinger equation in one dimension for cases where the particle's energy is both greater than and less than the potential energy.
This document discusses statistical mechanics and the distribution of energy among particles in a system. It provides 3 main types of statistical distributions based on the properties of identical particles: Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac statistics. Maxwell-Boltzmann statistics applies to distinguishable particles, while Bose-Einstein and Fermi-Dirac apply to indistinguishable particles (bosons and fermions respectively), with the key difference being that fermions obey the Pauli exclusion principle. The document also discusses applications of these distributions, including the Maxwell-Boltzmann distribution law for molecular energies in an ideal gas.
My introduction to electron correlation is based on multideterminant methods. I introduce the electron-electron cusp condition, configuration interaction, complete active space self consistent field (CASSCF), and just a little information about perturbation theories. These slides were part of a workshop I organized in 2014 at the University of Pittsburgh and for a guest lecture in a Chemical Engineering course at Pitt.
2. 1. Sarrera
Zinematika: partikulen higidura aztertu (arrazoirik gabe)
Dinamika: partikulen higiduraren eta higidura horren arrazoiaren arteko erlazioa aztertu.
Partikulen arteko elkarrekintzak: INDARRAK!!
Higiduraren legeak Isaac Newton-ek enuntziatu zituen (1686. urtean).
• Lege hauek c (argiaren abiadura hutsean) baino askoz astiroago higitzen diren
partikulentzat baino ez du balio.
• Transladatzen diren partikulentzat zein objektu makroskopikoentzat baliagarriak.
3. 2. Newton-en legeak
NEWTON-en 1. LEGEA: Inertziaren legea
“Gorputz baten gainean eragiten duen indarren erresultantea zero bada, gorputz hori
pausagunean dago edo higidura zuzen uniformearekin higitzen da.” INERTZIA
Partikula aske: indarrik jasaten ez duena.
Indarrik ez dagoenean gorputz batek ez du bere abiadura aldatzen.
Errealitatean: marruskadura-indarra.
NEWTON-en 2. LEGEA: Mekanika klasikoaren oinarrizko legea
“Gorputz baten higiduraren aldaketa, beraren gainean eragiten duen indarraren
proportzionala da eta indar horren norabide berdinean gertatzen da.”
“Gorputz baten gainean eragiten r duten F = m a r
indarren erresultantea berdin gorputz horren
masa bider daukan azelerazioa: .”
Indar bat baino gehiago daukagunean:
Partikula aske batentzat: 1N = 1kg m/s2
4. 2. Newton-en legeen analisia
r r
NEWTON-en 3. LEGEA: Akzio-erreakzio legea
“Indarrak beti bikoteka agertzen dira. Gorputz baten gainean indar bat eragiten badu
(akzioa), azken honek lehenengo gorputzaren gainean indar berdina baina aurkako
noranzkokoa eragingo du (erreakzioa).”
Garrantzitsua: - Akzioa eta erreakzioa ez dute gorputz berdinaren gainean eragiten.
- Akzio eta erreakzioa aldi berean gertatzen dira.
F = ma
Bakarrik da baliagarria masa kte-dun problemetan
(ez karga galtzen duten trenak, koheteak,...)
ES Inertzialei (ESI) lotutako behatzaileek bakarrik aplika dezakete.
r r r
F = ma r = {a r = A + a r '} = ma r ' = F '
Galileoren Erlatibitate printzipioa.
5. 3. Indarren adibideak
Lau oinarrizko interakzio (elkarrekintza)
GRABITATORIOA ELEKTROMAGNETIKOA NUKLEAR BORTITZA NUKLEAR AHULA
ITURRIA: karga ahula
masa (m) karga-elektrikoa (q) kolore-karga
(quarken ezaugarria)
Irispide luzekoak Irispide laburrekoak
Adibidez, elkarrekintza grabitatorioa:
F G mm r
r iturriekiko proportzionala
' ˆ g
2
r
= -
erakargarria
lotzen dituen norabidean
Berdin elkarrekintza elektrostatikoarentzat:
F k qq r
' ˆ q
' 2
r
=
r
6. 3. Indarren adibideak
Gorputz baten pisua
Gorputz baten eta Lurraren arteko elkarrekintza grabitatorioa da.
r P = mg
r
non g = 9.8 m/s2 lurraren kasurako.
Planetaren zentrorantz zuzenduta:
Malgukien indar elastikoa
Malgukiak egiten duen indarra, malgukiari bere l0 luzera naturala berreskuratze alderantz
eragiten du.
r
F
r
F
x
x
x
x
-x
l0
l
l
F = -kx
edo
Hook-en legea
Limite elastikoa
x
F
7. 3. Indarren adibideak
Tentsioak soketan
Indar hau soketan zehar hedatzen da. Soka idealak kontsideratuko ditugu.
Indar normala
r
T
P r
r
T
r
r
P r
r
T
r
' P r
T
T
T
r
2T
r
2T
m
N r
r
-N
N r
r
-N
Soka ideala: Masa arbuiagarria duena.
Kontaktuan dauden bi gorputzen artean agertzen den erreakzioa.
EZ DA BETI PISUAREN BERDINA!!!
8. Gorputz baten eta berarekin kontaktuan dagoen gainazalaren arteko irristatze erlatiboa
eragozten duen indarra.
msN
mdN
Pausagunea Higidura
3. Indarren adibideak
Irristatzearen aurkako marruskadura-indarra
r
Faplikatua
R F
r
Faplikatua
N r
r
R F
r
R -F
marruskadura-koefiziente
estatikoa
s d m > m
marruskadura-koefiziente
dinamikoa
Gainazalaren araberakoak dira
9. 4. Erreferentzia-sistema azeleratu baten
ESI Newton-en legeak bete!
ESI
dinamika
r a ' = 0 r
mgr
Lanpararen azelerazioa da.
ESeI
(ESI-etan)
Baina zer gertatzen da denean? Hau da, ESeI batetan?
INERTZIA-INDARRA
Adibideak:
A Lanpara bat bagoi azeleratu batean eskegita
A r
r
mgr
T
T
r
-mA
A r
Lanpara geldirik dago bagoiarekiko,
r
inertzia-indar bat jasaten du: -
m A .
Honek sortu
behatzen den
inklinazioa
10. 4. Erreferentzia-sistema azeleratu baten
dinamika
B Ardatz baten inguruan errotatzen duen objektu batek lotzen duen sokaren
tentsioa
ESI ESI
ESeI
r
T
w r
w r
r
T
r
-mA
Biratzerakoan objektuak azelerazio
normal bat du (sokaren tentsioak
sortua):
Objektuak ez du biratzen ESeI-arekiko,
inertzia-indar bat, indar
zentrifugoa, jasaten du.
