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Quantum Physics for Scientists and Technologists: Fundamental Principles and Applications for Biologists, Chemists, Computer Scientists, and Nanotechnologists by Paul Sanghera

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6

THE ANATOMY AND PHYSIOLOGY OF AN EQUATION

Politics is for the present, but an equation is for eternity.

Albert Einstein

Figure 6.0. One of six sculptures of Walk of Ideas in Berlin displaying the equivalence of mass and energy, unveiled on 19 May 2006.

Photo courtesy of Lienhard Schulz.

Einstein’s equation unifying the concept of mass and energy is the most famous equation in and outside the field of science. This chapter will introduce a not that famous equation, called Schrödinger equation, which captures the core principles of quantum mechanics. It may not be as popular as Einstein’s E = mc2 equation, but it is as central to quantum mechanics as Newton’s laws are to classical mechanics.

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In This Chapter

6.1 Introduction

6.2 The Schrödinger Wave Equation

6.3 The Schrödinger Equation for a Free Particle

6.4 Schrödinger Equation for a Particle in a Box

6.5 A Particle in a Three-Dimensional Box

6.6 Harmonic Oscillator

6.7 Understanding the Wave Function of a Harmonic Oscillator

6.8 Comparing Quantum Mechanical Oscillator with Classical Oscillator

6.9 Living in the Quantum World

6.10 Summary

6.11 Additional Problems

6.1 INTRODUCTION

As described in Chapter 5, a theory bases itself on a minimum number of assumptions from which other empirical principles and laws can be derived that may have previously been proposed to explain the experimental results and observations. Equations, ...

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