Foundations Of Quantum Mechanics: From Basics To Application

Foundations Of Quantum Mechanics: From Basics To Application
Published 3/2025
MP4 | Video: h264, 1920×1080 | Audio: AAC, 44.1 KHz

Lectures for a semester-long flipped course on quantum mechanics

What you’ll learn

Introduction to fundamental principles and the need for quantum mechanics

Domain of quantum mechanics and its applicability to microscopic systems

Complex numbers and their role in quantum mechanics

Concept and physical meaning of the wavefunction

Normalization of the wavefunction and its importance

Extracting position, velocity, and momentum from the wavefunction

Heisenberg’s uncertainty principle and its implications

Derivation and interpretation of Schrodinger’s equation

Superposition of stationary states and their physical consequences

Potential functions and their impact on quantum behavior

Orthogonality and completeness of quantum states

Fourier series applications in quantum mechanics

Quantum harmonic oscillator using ladder operators and power series solutions

Example computations and simulations for quantum systems
Requirements

Basic Mathematics – Algebra, trigonometry, and exponentials/logarithms

Complex Numbers – Understanding 𝑖 = − 1 i= −1 ​ and simple operations

Probability – Basic ideas of probability and distributions

Basic Physics – Newton’s laws, energy, and momentum

Description

Overview

Section 1: Introduction to Quantum Mechanics & Key Concepts

Lecture 1 Introduction to quantum mechanics

Lecture 2 The domain of quantum mechanics

Lecture 3 Key concepts in quantum mechanics

Section 2: Mathematical Foundations

Lecture 4 A review of complex numbers

Lecture 5 Complex numbers examples

Lecture 6 Probability in quantum mechanics

Lecture 7 Probability distributions and their properties

Lecture 9 Normalization of the wavefunction

Lecture 10 Position, velocity, and momentum from the wavefunction

Section 3: The Uncertainty Principle

Lecture 11 Introduction to the uncertainty principle

Lecture 12 Key concepts of QM, revisited

Section 4: The Schrödinger Equation

Lecture 14 Stationary solutions to the Schrödinger equation

Lecture 15 Superposition of stationary states

Lecture 16 Potential functions in the Schrödinger equation

Lecture 18 Infinite square well states, orthogonality and completeness (Fourier series)

Lecture 19 Infinite square well example computations and simulation