Understanding Quantum Science
A Concise Primer for Students of Chemistry, Biochemistry and Physics

Students are naturally drawn to quantum science by the intriguing behaviors of small particles. However, they can also be intimidated by the lengthy and complicated treatment found in the classroom. Understanding Quantum Science: A Concise Primer for Students of Chemistry, Biochemistry, and Physics is a highly accessible book that offers students an opportunity to grasp the most fascinating of quantum topics, without the intimidation. To be sure, math is necessary, but it is introduced as needed and kept concise. The emphasis is on the science: a certain differential equation can be solved, and when it is, we find the energies that hydrogen atom electrons are allowed to have. Each concept is developed in this manner, keeping focus on how and why it arises, and on the intriguing consequences.

This book provides a brief tour of some of the wonders of quantum science. But it is more than that, it is designed to be the most concise tour possible that truly explains how these wonders arise so that you can develop a working understanding of quantum concepts. If your goal is loftier and you wish to become a quantum specialist, the conceptual groundwork presented here, along with rationalization of the mathematics required, will position you well for higher level classes.

The Basics

1 Introducing Quantum Mechanics

2 The Schrödinger Equation

3 Deriving the Schröinger Equation

4 Operators, Oscillations, Uncertainty, and Quanta

5 Separation of Variables

6 ψ(x): General Conditions, Normalization, Bra-kets

One-Dimensional Potentials

7 Solving the TISE for the Simplest Potentials

8 The One-Dimensional Particle in a Box

9 The Formal Postulates of Quantum Mechanics

10 Simple Harmonic Oscillator (SHO): V = ½ kx2

Approximation Methods

11 Time-Independent Perturbation Theory (TIPT)

12 Time-Dependent Perturbation Theory (TDPT)

13 Variational Method

Three-Dimensional Space: Atoms and Molecules

14 Generalization to 3D

15 Angular Momentum

16 H-Atom: Solving the Radial TISE

17 Introduction to Multi-Electron Atoms, Molecules, and Spectroscopy

Steven M. Pascal is Professor of Chemistry and Biochemistry at Old Dominion University. He has previously taught medical students at the University of Rochester Medical Center, and physics students at Massey University in New Zealand. His previous book entitled NMR Primer: An HSQC Approach presents the basics of NMR needed by biological spectroscopists in a rigorous but mostly visual manner.