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Probability II  

Partition functions and wavefunctions

This chapter assesses partition functions and wavefunctions. Probability is best treated statistically when we deal with a vast number of particles. Statistical probabilities are usually considered in terms of a certainty or a proportion rather than simpler probabilities. The chapter then looks at the Boltzmann distribution, which describes the population of the energy levels which has the greatest weight and therefore the highest probability. We can further simplify the Boltzmann distribution by writing it in terms of the molecular partition function. The chapter also considers equilibrium constants, residual entropy, quantum mechanics, and tunnelling probability. Quantum tunnelling can occur when a particle tunnels through an energy barrier that classical mechanics would prevent.

Chapter

Cover The Chemistry Maths Book

Determinants  

This chapter takes a closer look at the theory of determinants, preparing the reader for the topic of matrix algebra. Determinants have certain symmetry properties that have made them an important tool in quantum mechanics. The chapter starts by explaining how the system of three linear equations in three unknowns can be solved. It also shows the solution of linear equations—introducing the Cramer's rule. The chapter also tackles the general properties of determinants such as transposition, multiplication by a constant, additional rule, interchange of rows or columns, equal two rows or columns, proportional rows or columns, among others. Furthermore, it explains the reduction of determinants to triangular form and describes alternating functions.