Dietterich Labs: Advanced Quantum Mechanics
Comprehensive video lectures covering advanced topics in quantum mechanics and relativistic quantum theory
About This Series
Dietterich Labs provides detailed, mathematically rigorous lectures on advanced quantum mechanics topics. These 37 lectures cover uncertainty principles, various solutions to the Schrödinger equation, perturbation theory, and relativistic quantum mechanics including the Klein-Gordon and Dirac equations.
📊 Mathematical Rigor
Detailed derivations and proofs throughout
🔬 Advanced Topics
Relativistic QM, Dirac equation, advanced perturbation theory
🎯 Problem-Solving
Step-by-step solutions to complex problems
Course Topics
Uncertainty Principles & Ehrenfest Theorem
Generalized Heisenberg Uncertainty Principle
Video Lecture
The Generalized Heisenberg Uncertainty Principle
Derivation of the generalized uncertainty relation for any two observables
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Energy-Time Uncertainty Principle
Video Lecture
Energy-Time Uncertainty Principle
Understanding ΔE·Δt ≥ ℏ/2 and its physical meaning
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Momentum Operator from Commutator
Video Lecture
Momentum Operator From The x-p Quantum Commutator
Deriving p̂ = -iℏ∂/∂x from [x̂,p̂] = iℏ
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Ehrenfest's Theorem (Momentum)
Video Lecture
Ehrenfest's Theorem (momentum)
d⟨p⟩/dt = ⟨-∇V⟩: quantum-classical correspondence
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Ehrenfest's Theorem (Position)
Video Lecture
Ehrenfest's Theorem (position)
d⟨x⟩/dt = ⟨p⟩/m: classical equations from QM
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Generalized Ehrenfest Theorem
Video Lecture
The Generalized Ehrenfest Theorem
Time evolution of expectation values for general observables
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Schrödinger Equation: Various Geometries
Möbius Strip
Video Lecture
Solving The Schrodinger Equation On A Mobius Strip
Quantum mechanics on non-orientable surfaces
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Quantum Harmonic Oscillator
Video Lecture
Quantum Harmonic Oscillator | Schrodinger Equation
Complete solution using ladder operators
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Electron in Magnetic Field
Video Lecture
An Electron In A Constant Magnetic Field
Landau levels and gauge invariance
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
On a Sphere
Video Lecture
Solving The Schrodinger Equation On A Sphere
Spherical harmonics and orbital angular momentum
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Cylindrical Infinite Well
Video Lecture
Electron In A Cylindrical Infinite Potential Well
Bessel functions and boundary conditions
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Spherical Infinite Well
Video Lecture
Electron In A Spherical Infinite Potential Well
Spherical Bessel functions
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Spherical Harmonic Oscillator
Video Lecture
Spherical Quantum Harmonic Oscillator
3D isotropic oscillator in spherical coordinates
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Angular Momentum & Quantum Rotors
Angular Momentum Operator Algebra
Video Lecture
Angular Momentum Operator Algebra And Eigenvalue Relations
[L_i, L_j] commutation relations via harmonic oscillator method
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Orbital Angular Momentum Eigenfunctions
Video Lecture
Orbital Angular Momentum Eigenfunctions
Spherical harmonics Y_ℓ^m(θ,φ)
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Quantum Rigid Rotor
Video Lecture
The Quantum Rigid Rotor
Molecular rotations and rotational spectra
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Hydrogen Atom & Central Potentials
Hydrogen Atom Solution
Video Lecture
How To Solve The Schrodinger Equation For The Hydrogen Atom
Complete derivation: Laguerre polynomials and energy levels
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Laplace-Runge-Lenz Vector
Video Lecture
Laplace–Runge–Lenz Vector Operator Relations
Hidden SO(4) symmetry of hydrogen atom
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Perturbation Theory & Applications
Wigner-Eckart Theorem
Video Lecture
Proving The Wigner-Eckart Theorem
Selection rules and reduced matrix elements
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Non-Degenerate Perturbation Theory
Video Lecture
Intro To Time Independent Non-Degenerate Perturbation Theory
First and second order corrections to energy
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Degenerate Perturbation Theory
Video Lecture
Intro To Degenerate Perturbation Theory
Lifting degeneracies and finding correct basis
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Linear Stark Effect
Video Lecture
The Linear Stark Effect
Hydrogen atom in electric field
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Hydrogen in Crystal Field
Video Lecture
Hydrogen Atom In A Crystal | Perturbation Theory | Wigner-Eckart
Crystal field splitting using Wigner-Eckart theorem
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Time Dependent PT (Part 1)
Video Lecture
Time Dependent Perturbation Theory Part 1: The Interaction Picture
Interaction picture and Schrödinger/Heisenberg pictures
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Time Dependent PT (Part 2)
Video Lecture
Time Dependent Perturbation Theory Part 2: The Dyson Series
Dyson series and Fermi's golden rule
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Shocking a Hydrogen Atom
Video Lecture
Shocking A Hydrogen Atom With An Electric Field
Sudden approximation and time-dependent fields
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Variational Method
Video Lecture
The Variational Method (QM approximation)
Upper bounds on ground state energy
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Relativistic Quantum Mechanics
Advanced topics: Klein-Gordon equation, Dirac equation, and their solutions for various systems. Essential preparation for quantum field theory.
Klein-Gordon on Sphere
Video Lecture
Solving The Klein-Gordon Equation On A Sphere
Relativistic scalar particles in spherical geometry
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Klein-Gordon Hydrogen Atom
Video Lecture
How To Solve The Klein-Gordon Equation For The Hydrogen Atom
Relativistic corrections to hydrogen spectrum
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Dirac Equation: Plane Waves
Video Lecture
Plane Wave Solutions To The Dirac Equation
Free particle solutions and spinor structure
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Relativistic Landau Levels
Video Lecture
Relativistic Landau Levels From The Dirac Equation
Dirac fermions in magnetic field
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Landau Levels: Power Series
Video Lecture
Relativistic Landau Levels + Dirac Equation: Power Series Method
Alternative solution method
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Landau Levels: Cylindrical Coords
Video Lecture
Dirac Landau Levels Using Cylindrical Coordinates
Cylindrical symmetry approach
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Dirac Hydrogen Atom
Video Lecture
How To Solve The Dirac Equation For The Hydrogen Atom
Fine structure from Dirac equation
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Spinor Spherical Harmonics
Video Lecture
Annoying Ass Spinor Spherical Harmonics Identity
Mathematical identities for Dirac solutions
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Dirac in 10 Coordinate Systems
Video Lecture
The Dirac Equation In Ten Different Coordinate Systems
General coordinate transformations for Dirac equation
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
Corrections & Details
Video Lecture
Did I Get This Right? Tell Me In The Comments
Additional details and corrections to previous lectures
💡 Tip: Watch at 1.25x or 1.5x speed for efficient learning. Use YouTube's subtitle feature if available.
How to Use These Lectures
For MIT 8.05/8.06 students: Use these as supplementary problem-solving examples, especially for perturbation theory and special geometries.
For QFT preparation: Focus on lectures 28-37 (relativistic QM) to build intuition for Klein-Gordon and Dirac fields before starting quantum field theory.
Advanced topics: Landau levels, Wigner-Eckart theorem, and crystal field theory connect to condensed matter physics and atomic physics.