Course8.04115 lectures28 h 20 min
Quantum Physics I
Prof. Barton Zwiebach · Massachusetts Institute of Technology
About
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.
Lectures
Part 1: Basic Concepts
- Quantum mechanics as a framework. Defining linearity
- Linearity and nonlinear theories. Schrödinger's equation
- Necessity of complex numbers
- Photons and the loss of determinism
- The nature of superposition. Mach-Zehnder interferometer
- More on superposition. General state of a photon and spin states
- Entanglement
- Mach-Zehnder interferometers and beam splitters
- Interferometer and interference
- Elitzur-Vaidman bombs
- The photoelectric effect
- Units of h and Compton wavelength of particles
- Compton Scattering
- de Broglie’s proposal
- de Broglie wavelength in different frames
- Galilean transformation of ordinary waves
- The frequency of a matter wave
- Group velocity and stationary phase approximation
- Motion of a wave-packet
- The wave for a free particle
- Momentum operator, energy operator, and a differential equation
- Free Schrödinger equation
- The general Schrödinger equation. x, p commutator
- Commutators, matrices, and 3-dimensional Schrödinger equation
- Interpretation of the wavefunction
- Normalizable wavefunctions and the question of time evolution
- Is probability conserved? Hermiticity of the Hamiltonian
- Probability current and current conservation
- Three dimensional current and conservation
- Wavepackets and Fourier representation
- Reality condition in Fourier transforms
- Widths and uncertainties
- Shape changes in a wave
- Time evolution of a free particle wavepacket
- Fourier transforms and delta functions
- Parseval identity
- Three-dimensional Fourier transforms
- Expectation values of operators
- Time dependence of expectation values
- Expectation value of Hermitian operators
- Eigenfunctions of a Hermitian operator
- Completeness of eigenvectors and measurement postulate
- Consistency condition. Particle on a circle
- Defining uncertainty
Part 2: Quantum Physics in One-dimensional Potentials
- Uncertainty and eigenstates
- Stationary states: key equations
- Expectation values on stationary states
- Comments on the spectrum and continuity conditions
- Solving particle on a circle
- Energy eigenstates for particle on a circle
- Infinite square well energy eigenstates
- Nodes and symmetries of the infinite square well eigenstates
- Finite square well. Setting up the problem
- Finite square well energy eigenstates
- Nondegeneracy of bound states in 1D. Real solutions
- Potentials that satisfy V(-x) = V(x)
- Qualitative insights: Local de Broglie wavelength
- Correspondence principle: amplitude as a function of position
- Local picture of the wavefunction
- Energy eigenstates on a generic symmetric potential. Shooting method
- Delta function potential I: Preliminaries
- Delta function potential I: Solving for the bound state
- Node Theorem
- Harmonic oscillator: Differential equation
- Behavior of the differential equation
- Recursion relation for the solution
- Quantization of the energy
- Algebraic solution of the harmonic oscillator
- Ground state wavefunction
- Number operator and commutators
- Excited states of the harmonic oscillator
- Creation and annihilation operators acting on energy eigenstates
- Scattering states and the step potential
- Step potential probability current
- Reflection and transmission coefficients
- Energy below the barrier and phase shift
- Wavepackets
- Wavepackets with energy below the barrier
- Particle on the forbidden region
- Waves on the finite square well
- Resonant transmission
- Ramsauer-Townsend phenomenology
- Scattering in 1D. Incoming and outgoing waves
- Scattered wave and phase shift
- Incident packet and delay for reflection
- Phase shift for a potential well
- Excursion of the phase shift
- Levinson's theorem, part 1
- Levinson's theorem, part 2
Part 3: One-dimensional Scattering, Angular Momentum, and Central Potentials
- Time delay and resonances
- Effects of resonance on phase shifts, wave amplitude and time delay
- Modelling a resonance
- Half-width and time delay
- Resonances in the complex k plane
- Translation operator. Central potentials
- Angular momentum operators and their algebra
- Commuting observables for angular momentum
- Simultaneous eigenstates and quantization of angular momentum
- Associated Legendre functions and spherical harmonics
- Orthonormality of spherical harmonics
- Effective potential and boundary conditions at r=0
- Hydrogen atom two-body problem
- Center of mass and relative motion wavefunctions
- Scales of the hydrogen atom
- Schrödinger equation for hydrogen
- Series solution and quantization of the energy
- Energy eigenstates of hydrogen
- Energy levels and diagram for hydrogen
- Degeneracy in the spectrum and features of the solution
- Rydberg atoms
- Orbits in the hydrogen atom
- More on the hydrogen atom degeneracies and orbits
- The simplest quantum system
- Hamiltonian and emerging spin angular momentum
- Eigenstates of the Hamiltonian
Syllabus and materials
At MIT OpenCourseWare, as the course publishes them.
Credits and licence
- Institution
- Massachusetts Institute of Technology
- Department
- Physics
- Teacher
- Prof. Barton Zwiebach
- Term
- Spring 2016
- Level
- Undergraduate
- Language
- English
- Subjects
- Physics
- Source
- MIT OpenCourseWare
- Licence
- CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
- Attribution
- Prof. Barton Zwiebach. Quantum Physics I. Spring 2016. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
- Who can watch
- MIT OpenCourseWare gives no rating. Invisible Network shows it to Teens profiles and older, judged from what the source says about it. How courses are placed
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