Intro to Quantum Mechanics

Quantum Mechanics Overview

• Deals with matter and energy at the atomic and subatomic levels.
• Explains the properties of microscopic systems like atoms and molecules.

Key Quantum Concepts

• Energy, momentum, and other properties are quantized, existing only in discrete values.
• Particles display both wave-like and particle-like characteristics.
• There's a limit to the precision of knowing certain pairs of properties simultaneously.
• A system can exist in multiple states at the same time.
• Systems can become correlated in ways not possible classically.

Schrödinger Equation

• Denotes a fundamental equation.
• Describes time evolution of a quantum system: $i\hbar\frac{\partial}{\partial t}\Psi(r,t) = \hat{H}\Psi(r,t)$.
• $i$ is the imaginary unit.
• $\hbar$ is the reduced Planck constant.
• $\Psi(r,t)$ is the wave function of the system.
• $\hat{H}$ is the Hamiltonian operator, total energy of the system.

Applications of Quantum Mechanics

• Understanding material properties at the atomic level in materials science
• Predicting chemical reactions and molecular properties in chemistry
• Designing electronic devices like transistors and semiconductors
• Quantum computing aims to develop computers solving unsolvable problems for classical computers.
• Developing medical imaging techniques like MRI and PET scans