In this chapter, the main features of quantum theory are presented. The chapter begins with a historical account of the invention of quantum mechanics. The meaning of position and momentum in quantum mechanics is discussed and non-commuting operators are introduced. The Schrödinger equation is presented and solved for a free particle and for a harmonic oscillator potential in one dimension. The meaning of the wavefunction is considered and the probabilistic interpretation is presented. The mathematical machinery and language of quantum mechanics are developed, including Hermitian operators, observables and expectation values. The uncertainty principle is discussed and the uncertainty relations are presented. Scattering and tunnelling by potential wells and barriers is considered. The use of variational principles to estimate ground state energies is explained and illustrated with a simple example.
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