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MITOCW 8.04 - Quantum physics I (Quantum mechanics as a framework.…
MITOCW 8.04 - Quantum physics I
Quantum mechanics as a framework. defining linearity
Linearity and nonlinear theories. Schrodinger's equation
Necessity of complex numbers
Photons and the loss of determinism
The nature of superpositions. Mach-Zehnder interferometer
More on superposition. General state of a photon and a spin states
Entaglement
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
Galilean transformation of ordinary waves
The frequency of matter wave
Group velocity and stationary phase approximation
Motion of wave-packet
The wave for a free particle
Momentum operator, energy operator, and a differential equation
Free Schrodinger equation
The general Schrodinger equation. x, p commutator
Commutators, matrices, and 3-dimensional Schrodinger equation
Interpretation of wave function
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 transform
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 transform
Expectation values 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
Defininf uncertainty
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
Correspondance principle: amplitude as a function of position
Local picture of the wavefunction
Energy eigenstates on a generic summetric potential. Shooting method
Delta function potential I: preliminaries
Delta function potential I: Solving for the bound state
Node theorems
Harmonic oscillator: Differential equation
Behaviour 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 coefficient
Energy below the barrier and phase shift
Wavepackets
Wavepackets with energy below barrier
Particle on the forbidden religion
Waves on the finite square well
Reasonant 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 potential well
Excursion of the phase shift
Levinson's theorem
Tie delay and resonances
Effects of resonance on phase shifts, wave amplitude and time delay
Modeling a resonance
Half-width and time delay
Resonance 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
Assiciated 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
Schrodinger equation for hydrogen
Series solutions 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