MIT 8.04 Quantum Physics I, Spring 2016 (English) (Part 2)

   Friday, December 13, 2024   

Starting a new Lecture Notes Series on MIT 8.04 Quantum Physics I, Spring 2016

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MIT 8.04 Quantum Physics I, Spring 2016 By Lecture Notes together!

Lecture 40: Expectation value of Hermitian operators

Lecture 41: Eigenfunctions of a Hermitian operator

Lecture 42: Completeness of eigenvectors and measurement postulate

Lecture 43: Consistency condition. Particle on a circle

Lecture 44: Defining uncertainty

Lecture 45: Uncertainty and eigenstates

Lecture 46: Stationary states: key equations

Lecture 47: Expectation values on stationary states

Lecture 48: Comments on the spectrum and continuity conditions

Lecture 49: Solving particle on a circle

Lecture 50: Energy eigenstates for particle on a circle

Lecture 51: Infinite square well energy eigenstates

Lecture 52: Nodes and symmetries of the infinite square well eigenstates

Lecture 53: Finite square well. Setting up the problem

Lecture 54: Finite square well energy eigenstates

Lecture 55: Nondegeneracy of bound states in 1D. Real solutions

Lecture 56: Potentials that satisfy V(-x) = V(x)

Lecture 57: Qualitative insights: Local de Broglie wavelength

Lecture 58: Correspondence principle: amplitude as a function of position

Lecture 59: Local picture of the wavefunction

Lecture 60: Energy eigenstates on a generic symmetric potential. Shooting method

Lecture 61: Delta function potential I: Preliminaries

Lecture 62: Delta function potential I: Solving for the bound state

Lecture 63: Node Theorem

Lecture 64: Harmonic oscillator: Differential equation

Lecture 65: Behavior of the differential equation

Lecture 66: Recursion relation for the solution

Lecture 67: Quantization of the energy

Lecture 68: Algebraic solution of the harmonic oscillator

Lecture 69: Ground state wavefunction

Lecture 70: Number operator and commutators

Lecture 71: Excited states of the harmonic oscillator

Lecture 72: Creation and annihilation operators acting on energy eigenstates

Lecture 73: Scattering states and the step potential

Lecture 74: Step potential probability current

Lecture 75: Reflection and transmission coefficients

Lecture 76: Energy below the barrier and phase shift

Lecture 77: Wavepackets

Lecture 78: Wavepackets with energy below the barrier