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Uedu Open / Quantum Physics I
8.04

Quantum Physics I

Prof. Barton Zwiebach | Spring 2016
Science & Math Physics Quantum Mechanics Science
前往原始課程
CC BY-NC-SA 4.0
課程簡介

This is the first course in the undergraduate Quantum Physics sequence. It introduces the basic features of quantum mechanics. It covers the experimental basis of quantum physics, introduces wave mechanics, Schrödinger’s equation in a single dimension, and Schrödinger’s equation in three dimensions. The lectures and lecture notes for this course form the basis of Zwiebach’s textbook Mastering Quantum Mechanics published by MIT Press in April 2022.

This presentation of 8.04 by Barton Zwiebach (2016) differs somewhat and complements nicely the presentation of Allan Adams (2013). Adams covers a larger set of ideas; Zwiebach tends to go deeper into a smaller set of ideas, offering a systematic and detailed treatment. Adams begins with the subtleties of superpostion, while Zwiebach discusses the surprises of interaction-free measurements. While both courses overlap over a sizable amount of standard material, Adams discussed applications to condensed matter physics, while Zwiebach focused on scattering and resonances. The different perspectives of the instructors make the problem sets in the two courses rather different.

課程資訊
來源MIT 開放式課程
科系Physics
語言English
影片數115
課程影片 (115)
1
Quantum mechanics as a framework. Defining linearity
Quantum mechanics as a framework. Defining linearity
2
Linearity and nonlinear theories. Schrödinger's equation
Linearity and nonlinear theories. Schrödinger's equation
3
Necessity of complex numbers
Necessity of complex numbers
4
Photons and the loss of determinism
Photons and the loss of determinism
5
The nature of superposition. Mach-Zehnder interferometer
The nature of superposition. Mach-Zehnder interferometer
6
More on superposition. General state of a photon and spin states
More on superposition. General state of a photon and spin states
7
Entanglement
Entanglement
8
Mach-Zehnder interferometers and beam splitters
Mach-Zehnder interferometers and beam splitters
9
Interferometer and interference
Interferometer and interference
10
Elitzur-Vaidman bombs
Elitzur-Vaidman bombs
11
The photoelectric effect
The photoelectric effect
12
Units of h and Compton wavelength of particles
Units of h and Compton wavelength of particles
13
Compton Scattering
Compton Scattering
14
de Broglie’s proposal
de Broglie’s proposal
15
de Broglie wavelength in different frames
de Broglie wavelength in different frames
16
Galilean transformation of ordinary waves
Galilean transformation of ordinary waves
17
The frequency of a matter wave
The frequency of a matter wave
18
Group velocity and stationary phase approximation
Group velocity and stationary phase approximation
19
Motion of a wave-packet
Motion of a wave-packet
20
The wave for a free particle
The wave for a free particle
21
Momentum operator, energy operator, and a differential equation
Momentum operator, energy operator, and a differential equation
22
Free Schrödinger equation
Free Schrödinger equation
23
The general Schrödinger equation. x, p commutator
The general Schrödinger equation. x, p commutator
24
Commutators, matrices, and 3-dimensional Schrödinger equation
Commutators, matrices, and 3-dimensional Schrödinger equation
25
Interpretation of the wavefunction
Interpretation of the wavefunction
26
Normalizable wavefunctions and the question of time evolution
Normalizable wavefunctions and the question of time evolution
27
Is probability conserved? Hermiticity of the Hamiltonian
Is probability conserved? Hermiticity of the Hamiltonian
28
Probability current and current conservation
Probability current and current conservation
29
Three dimensional current and conservation
Three dimensional current and conservation
30
Wavepackets and Fourier representation
Wavepackets and Fourier representation
31
Reality condition in Fourier transforms
Reality condition in Fourier transforms
32
Widths and uncertainties
Widths and uncertainties
33
Shape changes in a wave
Shape changes in a wave
34
Time evolution of a free particle wavepacket
Time evolution of a free particle wavepacket
35
Fourier transforms and delta functions
Fourier transforms and delta functions
36
Parseval identity
Parseval identity
37
Three-dimensional Fourier transforms
Three-dimensional Fourier transforms
38
Expectation values of operators
Expectation values of operators
39
Time dependence of expectation values
Time dependence of expectation values
40
Expectation value of Hermitian operators
Expectation value of Hermitian operators
41
Eigenfunctions of a Hermitian operator
Eigenfunctions of a Hermitian operator
42
Completeness of eigenvectors and measurement postulate
Completeness of eigenvectors and measurement postulate
43
Consistency condition. Particle on a circle
Consistency condition. Particle on a circle
44
Defining uncertainty
Defining uncertainty
45
Uncertainty and eigenstates
Uncertainty and eigenstates
46
Stationary states: key equations
Stationary states: key equations
47
Expectation values on stationary states
Expectation values on stationary states
48
Comments on the spectrum and continuity conditions
Comments on the spectrum and continuity conditions
49
Solving particle on a circle
Solving particle on a circle
50
Energy eigenstates for particle on a circle
Energy eigenstates for particle on a circle
51
Infinite square well energy eigenstates
Infinite square well energy eigenstates
52
Nodes and symmetries of the infinite square well eigenstates
Nodes and symmetries of the infinite square well eigenstates
53
Finite square well. Setting up the problem
Finite square well. Setting up the problem
54
Finite square well energy eigenstates
Finite square well energy eigenstates
55
Nondegeneracy of bound states in 1D. Real solutions
Nondegeneracy of bound states in 1D. Real solutions
56
Potentials that satisfy V(-x) = V(x)
Potentials that satisfy V(-x) = V(x)
57
Qualitative insights: Local de Broglie wavelength
Qualitative insights: Local de Broglie wavelength
58
Correspondence principle: amplitude as a function of position
Correspondence principle: amplitude as a function of position
59
Local picture of the wavefunction
Local picture of the wavefunction
60
Energy eigenstates on a generic symmetric potential. Shooting method
Energy eigenstates on a generic symmetric potential. Shooting method
61
Delta function potential I: Preliminaries
Delta function potential I: Preliminaries
62
Delta function potential I: Solving for the bound state
Delta function potential I: Solving for the bound state
63
Node Theorem
Node Theorem
64
Harmonic oscillator: Differential equation
Harmonic oscillator: Differential equation
65
Behavior of the differential equation
Behavior of the differential equation
66
Recursion relation for the solution
Recursion relation for the solution
67
Quantization of the energy
Quantization of the energy
68
Algebraic solution of the harmonic oscillator
Algebraic solution of the harmonic oscillator
69
Ground state wavefunction
Ground state wavefunction
70
Number operator and commutators
Number operator and commutators
71
Excited states of the harmonic oscillator
Excited states of the harmonic oscillator
72
Creation and annihilation operators acting on energy eigenstates
Creation and annihilation operators acting on energy eigenstates
73
Scattering states and the step potential
Scattering states and the step potential
74
Step potential probability current
Step potential probability current
75
Reflection and transmission coefficients
Reflection and transmission coefficients
76
Energy below the barrier and phase shift
Energy below the barrier and phase shift
77
Wavepackets
Wavepackets
78
Wavepackets with energy below the barrier
Wavepackets with energy below the barrier
79
Particle on the forbidden region
Particle on the forbidden region
80
Waves on the finite square well
Waves on the finite square well
81
Resonant transmission
Resonant transmission
82
Ramsauer-Townsend phenomenology
Ramsauer-Townsend phenomenology
83
Scattering in 1D. Incoming and outgoing waves
Scattering in 1D. Incoming and outgoing waves
84
Scattered wave and phase shift
Scattered wave and phase shift
85
Incident packet and delay for reflection
Incident packet and delay for reflection
86
Phase shift for a potential well
Phase shift for a potential well
87
Excursion of the phase shift
Excursion of the phase shift
88
Levinson's theorem, part 1
Levinson's theorem, part 1
89
Levinson's theorem, part 2
Levinson's theorem, part 2
90
Time delay and resonances
Time delay and resonances
91
Effects of resonance on phase shifts, wave amplitude and time delay
Effects of resonance on phase shifts, wave amplitude and time delay
92
Modelling a resonance
Modelling a resonance
93
Half-width and time delay
Half-width and time delay
94
Resonances in the complex k plane
Resonances in the complex k plane
95
Translation operator. Central potentials
Translation operator. Central potentials
96
Angular momentum operators and their algebra
Angular momentum operators and their algebra
97
Commuting observables for angular momentum
Commuting observables for angular momentum
98
Simultaneous eigenstates and quantization of angular momentum
Simultaneous eigenstates and quantization of angular momentum
99
Associated Legendre functions and spherical harmonics
Associated Legendre functions and spherical harmonics
100
Orthonormality of spherical harmonics
Orthonormality of spherical harmonics
101
Effective potential and boundary conditions at r=0
Effective potential and boundary conditions at r=0
102
Hydrogen atom two-body problem
Hydrogen atom two-body problem
103
Center of mass and relative motion wavefunctions
Center of mass and relative motion wavefunctions
104
Scales of the hydrogen atom
Scales of the hydrogen atom
105
Schrödinger equation for hydrogen
Schrödinger equation for hydrogen
106
Series solution and quantization of the energy
Series solution and quantization of the energy
107
Energy eigenstates of hydrogen
Energy eigenstates of hydrogen
108
Energy levels and diagram for hydrogen
Energy levels and diagram for hydrogen
109
Degeneracy in the spectrum and features of the solution
Degeneracy in the spectrum and features of the solution
110
Rydberg atoms
Rydberg atoms
111
Orbits in the hydrogen atom
Orbits in the hydrogen atom
112
More on the hydrogen atom degeneracies and orbits
More on the hydrogen atom degeneracies and orbits
113
The simplest quantum system
The simplest quantum system
114
Hamiltonian and emerging spin angular momentum
Hamiltonian and emerging spin angular momentum
115
Eigenstates of the Hamiltonian
Eigenstates of the Hamiltonian