Introduction to Quantum Mechanics/Chapter 1

Introduction to Quantum Mechanics

• Part I: Theory
  • 1. The Wave Function
  • 2. The Time-Indepedent Schrodinger Function
  • 3. Formalism
  • 4. Quantum Mechanics in Three Dimensions
  • 5. Identical Particles
• Part II: Applications
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.

Notes

The Schrodinger Wave Equation:

<math>i\hbar {\partial \Psi \over \partial t} = - {\hbar^2 \over 2m} {\partial^2 \Psi \over \partial x^2} + V \Psi</math>

• <math>\Psi(x,t)</math>: The wave function, varies over position and time.
• <math>i = \sqrt{-1}</math>
• <math>\hbar = {h \over 2\pi} = 1.054573 \times 10^{-34}\ J\ s</math>, Planck's Constant.
• <math>m</math>, mass of the particle.
• <math>V(x,t)</math>, the potential.

This is probably the first time you're seeing something like this, so don't let it overhwelm you.

The wave function itself is somewhat meaningless. We'll talk about how we can get physical things we are familiar with, like position and momentum, out of it.

This is a second-order differential equation. They are not trivial to solve, particular for non-trivial V.