chapter  1
Introduction and review of quantum mechanics
Pages 18

The application of quantum theory to solids has revolutionised the understanding of materials and played a pivotal role in the information revolution of the last fifty years. Quantum mechanical properties are measurable on a macroscopic scale in superconductors, allowing both the determination of fundamental constants and the commercial development of technologies such as magnetic resonance imaging. As quantum mechanics treats particles as waves, it is useful to review some of the key properties of waves. A particle must now be described by a wavepacket, and any wavepacket is always spread over some region of space. There are several 'tricks' based on the general properties of wavefunctions which are useful when solving and applying Schrodinger's equation. As the ground state wavefunction is always even in a symmetric potential, choosing an odd function allows an estimate of the first excited state energy.