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Lecture
Quantum Mechanics: Schrödinger Equation
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Quantum Mechanics: Schrödinger Equation
Explores the Schrödinger equation in quantum mechanics, emphasizing conservation of probability and numerical schemes.
Numerical Methods: Euler and Crank-Nicolson
Covers Euler and Crank-Nicolson methods for solving differential equations.
Quantum Mechanics: Principles and Operators
Covers wave functions, electron density, probability distributions, and quantum operators.
System of ODEs
Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.
Numerical Methods for Boundary Value Problems
Covers numerical methods for solving boundary value problems using finite difference, FFT, and finite element methods.
Quantum Mechanics Evolution
Explains the representation for evolution in quantum mechanics and the application of path integrals.
Numerical Methods for Schrödinger Equation
Explores numerical methods for solving the time-dependent Schrödinger equation using grid representation and split-operator algorithms.
Quantum Mechanics: Path Integral Formulation
Covers the path integral formulation of Quantum Mechanics, emphasizing its advantages and connection with statistical mechanics.
Error Estimation in Numerical Methods
Explores error estimation in numerical methods for solving ordinary differential equations, emphasizing the impact of errors on solution accuracy and stability.
Wave Equation Stability
Explores the stability of the wave equation finite difference scheme and resonant excitation.
