This chapter discusses the central concepts and equations of quantum theory which
demonstrates how particles spread through space like waves and are described mathematically
by a wavefunction. It examines how the wavefunction is interpreted and introduces the
uncertainty principle, which is one of the most profound departures of quantum mechanics
from classical mechanics. It also highlights the dynamical properties of a system that are
contained in the wavefunction and are obtained by solving the Schrödinger equation. The
chapter reconciles the facts that atoms and molecules can possess only certain energies,
that waves exhibit the properties of particles, and that particles exhibit the properties of
waves. It reviews the classical concept that have been accommodated by the development of
quantum mechanics, in which equations are set up to treat a particle as spread through space
like a wave.

### Chapter

## The dynamics of microscopic systems

### Chapter

## The quantum mechanics of motion

This chapter pays particular attention to the quantum mechanics of motion. It is not possible to explain the structures and properties of atoms and molecules, where the role of electrons is central, without using quantum mechanics. Many of the processes of biochemistry involve the transfer of electrons and protons from a donor to an acceptor, and this migration can be understood only in terms of quantum theory. Here, the chapter introduces three fundamental types of motion — translation, rotation, and vibration — along with their characteristic quantum mechanical behaviours. It shows how various unexpected properties emerge, such as the ability of particles to penetrate into classically forbidden regions, the quantization of energy and angular momentum, and the existence of energy that cannot be removed from the system.

### Chapter

## Wavefunctions

This chapter examines the interpretation of the wavefunction, and specifically what
it reveals about the location of a particle. In quantum mechanics, all the
properties of a system are expressed in terms of a wavefunction, which is obtained
by solving the equation proposed by Erwin Schrödinger. Indeed, wavefunctions provide
the essential foundation for understanding the properties of electrons in atoms and
molecules, and are central to explanations in chemistry. The chapter then considers
how, according to the Born interpretation, the probability density at a point is
proportional to the square of the wavefunction at that point. A wavefunction is
normalized if the integral over all space of its square modulus is equal to 1.
Ultimately, a wavefunction must be single-valued, continuous, not infinite over a
finite region of space, and have a continuous slope. The quantization of energy
stems from the constraints that an acceptable wavefunction must satisfy.

### Chapter

## Translation

This chapter describes a particle confined to a finite region of space that can possess
only certain discrete energies. It also looks at the corresponding wavefunctions. It
analyzes the quantization of energy that emerges as a natural consequence of solving the
Schrödinger equation and the conditions imposed on it. It also introduces a striking
non-classical feature of small particles, which describes their ability to penetrate into
and through regions where classical physics would forbid them to be found. The chapter talks
about the translational energy levels of a particle which are confined to a finite region of
space and are quantized. It explores how quantum mechanics reveal the ability of a particle
to penetrate into and through regions where classical physics would forbid it to be
found.

### Chapter

## Translational motion

This chapter evaluates translational motion, motion through space, which is one of
the fundamental types of motion treated by quantum mechanics. According to quantum
theory, a particle constrained to move in a finite region of space is described by
only certain wavefunctions and can possess only certain energies. That is,
quantization emerges as a natural consequence of solving the Schrödinger equation
and the conditions imposed on it. The solutions also expose a number of
non-classical features of particles, especially their ability to tunnel into and
through regions where classical physics would forbid them to be found. Light
particles are more able to tunnel through barriers than heavy ones. The chapter also
considers the occurrence of degeneracy, which is a consequence of the symmetry of
the system.

### Chapter

## Operators and observables

This chapter explains that a central feature of quantum theory is its
representation of observables by ‘operators’, which act on the wavefunction and
extract the information it contains. It shows how operators are constructed and
used. Observables are represented by hermitian operators, which have real
eigenvalues and orthogonal eigenfunctions. When the system is not described by a
single eigenfunction of an operator, it may be expressed as a superposition of such
eigenfunctions. One consequence of the use of operators is the ‘uncertainty
principle’, one of the most profound departures of quantum mechanics from classical
mechanics. The uncertainty principle restricts the precision with which
complementary observables may be specified and measured simultaneously.

### Chapter

## The origins of quantum mechanics

This chapter traces the origins of quantum mechanics. The classical mechanics
developed by Isaac Newton in the seventeenth century is an extraordinarily
successful theory for describing the motion of everyday objects and planets.
However, late in the nineteenth century, scientists started to make observations
that could not be explained by classical mechanics. They were forced to revise their
entire conception of the nature of matter and replace classical mechanics by a
theory that became known as quantum mechanics. The chapter begins by looking at
energy quantization, considering black-body radiation, heat capacity, and atomic and
molecular spectra. It then discusses wave–particle duality, which is the recognition
that the concepts of particle and wave blend together.

### Book

### Peter Atkins, Julio de Paula, and Ronald Friedman

Physical Chemistry starts off by looking at the foundations of the subject and provides the reader with some mathematical background. It then looks at quantum mechanics, taking into consideration the quantum mechanics of motion, molecular structure, and molecular symmetry. It then considers Fourier transforms, molecular spectroscopy, magnetic resonance, statistical thermodynamics, probability theory, the first law of thermodynamics, and multivariate calculus. The final part of the book examines physical equilibria, chemical equilibria, molecular motion, chemical kinetics, reaction dynamics, and processes in fluid systems and solid states.