Lectures related to Stochastic Numerical Methods for Many-Body Quantum Systems

Quantum Science: The Electron and Its Wave-Particle Duality

Provides an overview of the electron's role in quantum science, focusing on its wave-particle duality and the mathematical framework of quantum mechanics.

Quantum Mechanics Basics

Covers the basics of quantum mechanics, focusing on solving the non relativistic Schrodinger equation.

Quantum Physics I

Covers the basics of quantum physics, focusing on the quantum harmonic oscillator and eigen-kets of Hamiltonian.

Iterative Solvers: Eigenvalue Problems

Delves into iterative solvers for eigenvalue problems, addressing user criteria, convergence metrics, and method choices.

Quantum Chemistry: Eigenfunctions and Operators

Explores eigenfunctions and operators in quantum chemistry, emphasizing their significance in understanding bound states.

Reminders on two-level systems

Covers the basics of two-level systems, including states, operators, and the Bloch Sphere.

Quantum Mechanics: Harmonic Oscillator and Molecular Interactions

Discusses the harmonic oscillator in quantum mechanics and its implications for molecular interactions and energy levels.

Numerical Analysis: Linear Systems

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Jarzynski Equation and Quantum Circuits

Explores the Jarzynski equation and the quantization of electrical circuits in quantum harmonic oscillators.

Convergence Analysis: Iterative Methods

Covers the convergence analysis of iterative methods and the conditions for convergence.

Quantum Bound States

Explores quantum bound states, energy levels, and superposition in molecular bonding.

Quantum Dynamics: Exact Methods and Applications

Covers exact and semiclassical quantum dynamics, including Schrödinger's equation and molecular interactions.

Quantum Mechanics: Electron Propagation and Measurement

Covers electron propagation, quantum operators, and the measurement process in quantum mechanics.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Dirac Notation and TDSE Solutions

Reviews Dirac notation, observable operators, and exact TDSE solutions using basis sets and Hamiltonians.

Value Iteration Acceleration: PID and Operator Splitting

Explores accelerating the Value Iteration algorithm using control theory and matrix splitting techniques to achieve faster convergence.

Eigenvalue Problems: Methods and Applications

Explores eigenvalue problems, iterative methods, and their applications in quantum physics and network analysis.

Quantum Mechanics: Wave Functions and Operators

Explores quantum mechanics, focusing on wave functions, operators, Heisenberg uncertainty principle, and particles in potential wells.

Harmonic Oscillators: Definitions and Dynamics

Covers the definitions and dynamics of harmonic oscillators, including ladder operators and coherent states.

Advanced General Chemistry I

Explores wave functions, electron density, quantum mechanics principles, operators, Schrödinger's equation, and key quantum terminologies.