Chapter 7

The Linear Vector Space

You see things that are and say ‘Why?’ But I dream things that never were and say ‘Why not?’

George Bernard Shaw

7.1  INTRODUCTION

In Chapters 2 and 3, while discussing the formation of a wave-packet, which represents a moving particle, we found the wave packet might be formed out of a large number of plane wave components. In fact, the state of a particle may be represented by a simple plane wave or by a combination of two or large number of plane waves (in the form of a wave packet) depending upon the form of the potential in which the particle is moving. The state of the particle is obtained by solving the corresponding Schrodinger equation of the particle. The Schrodinger equation [Eq. (4.25)] is a linear ...

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