Introducing quantum mechanics immediately after considering the issue of cell division and cell-cell recognition, with their associated complex structures and structural changes, is rather shocking. “Continuum” normally refers to the continuous allowed values of energy of a quantum particle once its energy becomes positive. Electrons bound to atoms have negative total energies, indicating they are in bound states. Stationary states of relevance in biophysics usually occur in cases of electrons or protons bound to atoms or molecules. The chapter examines some interesting and apparently complicated cases in photosynthesis and heme proteins. Symmetry is an important concept in both quantum mechanics and in biosystems. Collisions of atoms constantly occur in gases, liquids, and solids. Particle collisions are the bread and butter of particle physics. The discovery of the “Rutherford atom” was made by collision experiments, Rutherford scattering, and first showed that an atom had a small, heavy nucleus surrounded by light electrons.
Introducing quantum mechanics immediately after considering the issue of cell division and cell-cell recognition, with their associated complex structures and structural changes, is rather shocking. “Continuum” normally refers to the continuous allowed values of energy of a quantum particle once its energy becomes positive. Electrons bound to atoms have negative total energies, indicating they are in bound states. Stationary states of relevance in biophysics usually occur in cases of electrons or protons bound to atoms or molecules. The chapter examines some interesting and apparently complicated cases in photosynthesis and heme proteins. Symmetry is an important concept in both quantum mechanics and in biosystems. Collisions of atoms constantly occur in gases, liquids, and solids. Particle collisions are the bread and butter of particle physics. The discovery of the “Rutherford atom” was made by collision experiments, Rutherford scattering, and first showed that an atom had a small, heavy nucleus surrounded by light electrons.
In 1897, Thomson demonstrated that cathode rays (observed to be emitted from the cathodes of vacuum tubes) were in fact charged particles which he called electrons. Thomson proposed that the atom consisted of a positively charged sphere in which were embedded negatively charged electrons. Rutherford subsequently found in 1911 that the electrons orbited at some distance from a central positively charged nucleus. Rutherford proposed that electrostatic attraction between the nucleus and the electron was balanced by the centrifugal force arising from the orbital motion. However, if this were the case, then the electrons (being accelerated inwards towards the center of rotation) would continuously radiate all their energy as electromagnetic waves and very quickly fall into the nucleus. In 1913, Bohr postulated two important additions to Rutherford’s theory of atomic structure: 1. Electrons can orbit the nucleus in what are called stationary states in which no emission of radiation occurs and in which the angular momentum L is constrained to have values: 2. Electrons can make transitions from one state to another accompanied by the emission or absorption of a single photon of energy E = hf thus leading to absorption and emission spectra.
Anatomy of an atom In the second half of my story, the three strands of relativity, quantization and symmetry will be braided together. Before we embark on this journey, let us take a rest and consider some ways in which the properties of the small-scale quantum world govern our world at large. Most people wonder about the relevance of subatomic studies for our understanding of ourselves. Quite a few popular accounts of particle physics contain a heavy dose of reflections upon Larger Issues and related Deep Thoughts. I will try to avoid that, but it cannot be denied that the connections between the subatomic scale and our daily world are strong and direct, albeit invisible to our large-scale senses. Let us first consider atoms, the building blocks that have the most direct significance in our daily lives (in the remaining chapters we will discuss the structure of the particles of which atoms are made). For simplicity and definiteness, and because we have encountered it in previous discussions, I will mainly speak of the hydrogen atom. Its nucleus is a proton, having one unit of positive electric charge. A neutral hydrogen atom is formed when an electron, bearing one negative unit of electric charge, binds to it. The binding makes the atom electrically neutral.
The early twentieth century was a revolutionary time in the history of physics. People often think of Einstein's special theory of relativity of 1905, which changed our conceptions of time and space. But among physicists, quantum mechanics is usually regarded as an even more radical change in our thinking about the physical world. Quantum mechanics, which was developed between 1900 and 1926, began as a theory of atoms and light but has now become the framework in terms of which all basic physical theories are expected to be cast. We need quantum ideas not only to understand atoms, molecules, and elementary particles, but also to understand the electronic properties of solids and even certain astronomical phenomena such as the stability of white dwarf stars. The theory was radical in part because it introduced probabilistic behavior as a fundamental aspect of the world, but even more because it seems to allow mutually exclusive situations to exist simultaneously in a “quantum superposition.” We will see later that the possibility of quantum superposition is largely responsible for a quantum computer's distinctive advantage over an ordinary computer. The present chapter is devoted to introducing the basic principles of quantum mechanics. There are essentially four components of the mathematical structure of quantum mechanics. We need to know how to represent (i) states, (ii) measurements, (iii) reversible transformations, and (iv) composite systems. We will develop the first three in stages, starting with a very simple case – linear polarization of photons – and working toward the most general case.
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and the processes by which these arrangements change. This comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions. The term atomic physics can be associated with nuclear power and nuclear weapons, due to the synonymous use of atomic and nuclear in Standard English. Physicists distinguish between atomic physics -which deals with the atom as a system consisting of a nucleus and electrons- and nuclear physics, which studies nuclear reactions and special properties of atomic nuclei. As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular, and optical physics. Physics research groups are usually so classified. Atomic physics primarily considers atoms in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules (although much of the physics is identical), nor does it examine atoms in a solid state as condensed matter. It is concerned with processes such as ionization and excitation by photons or collisions with atomic particles. While modelling atoms in isolation may not seem realistic, if one considers atoms in a gas or plasma then the time-scales for atom-atom interactions are huge in comparison to the atomic processes that are generally considered. This means that the individual atoms can be treated as if each were in isolation, as the vast majority of the time they are. By this consideration atomic physics provides the underlying theory in plasma physics and atmospheric physics, even though both deal with very large numbers of atoms. Electrons form notional shells around the nucleus. These are normally in a ground state but can be excited by the absorption of energy from light (photons), magnetic fields, or interaction with a colliding particle (typically ions or other electrons). Electrons that populate a shell are said to be in a bound state. The energy necessary to remove an electron from its shell (taking it to infinity) is called the binding energy. Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy. The atom is said to have undergone the process of ionization. If the electron absorbs a quantity of energy less than the binding energy, it will be transferred to an excited state. After a certain time, the electron in an excited state will "jump" (undergo a transition) to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, since energy is conserved. If an inner electron has absorbed more than the binding energy (so that the atom ionizes), then a more outer electron may undergo a transition to fill the inner orbital. In this case, a visible photon or a characteristic x-ray is emitted, or a phenomenon known as the Auger effect may take place, where the released energy is transferred to another bound electron, causing it to go into the continuum. The Auger effect allows one to multiply ionize an atom with a single photon. There are rather strict selection rules as to the electronic configurations that can be reached by excitation by light — however there are no such rules for excitation by collision processes. One of the earliest steps towards atomic physics was the recognition that matter was composed of atoms. It forms a part of the texts written in 6th century BC to 2nd century BC such as those of Democritus or Vaisheshika Sutra written by Kanad. This theory was later developed in the modern sense of the basic unit of a chemical element by the British chemist and physicist John Dalton in the 18th century. At this stage, it wasn't clear what atoms were although they could be described and classified by their properties (in bulk). The invention of the periodic system of elements by Mendeleev was another great step forward. The true beginning of atomic physics is marked by the discovery of spectral lines and attempts to describe the phenomenon, most notably by Joseph von Fraunhofer. The study of these lines led to the Bohr atom model and to the birth of quantum mechanics. In seeking to explain atomic spectra an entirely new mathematical model of matter was revealed. As far as atoms and their electron shells were concerned, not only did this yield a better overall description, i.e. the atomic orbital model, but it also provided a new theoretical basis for chemistry (quantum chemistry) and spectroscopy. Since the Second World War, both theoretical and experimental fields have advanced at a rapid pace. This can be attributed to progress in computing technology, which has allowed larger and more sophisticated models of atomic structure and associated collision processes. Similar technological advances in accelerators, detectors, magnetic field generation and lasers have greatly assisted experimental work.
An atom consists of a nucleus, containing protons and neutrons, with various electrons swarming around the outskirts. The electrons are held in the vicinity of the nucleus as they are negatively charged and hence attracted by the positively charged protons. Although atoms are complicated objects, there are certain situations where they can be treated as simple lumps of matter. Their internal structure has no relevance to the details of what is happening. This sort of situation is exemplified by experiments in which atoms are deliberately smashed into one another at comparatively low energy and as such provide an ideal start in a study of the quantum physics of identical particles. When we are dealing with atoms, there is something more to being ‘identical’ than we can appreciate with larger-scale objects. Atoms of the same type are really identical, measurably identical if you like, which can make a considerable difference in some physically important situations.
Introduction It is believed that the basic physical building blocks forming the world we live in may be categorized into particles of matter and carriers of force between matter. All known elementary constituents of matter and transmitters of force are quantized. For example, energy, momentum, and angular momentum take on discrete quantized values. The electron is an example of an elementary particle of matter, and the photon is an example of a transmitter of force. Neutrons, protons, and atoms are composite particles made up of elementary particles of matter and transmitters of force. These composite particles are also quantized. Because classical mechanics is unable to explain quantization, we must learn quantum mechanics in order to understand the microscopic properties of atoms – which, for example, make up solids such as crystalline semiconductors. Historically, the laws of quantum mechanics have been established by experiment. The most important early experiments involved light. Long before it was realized that light waves are quantized into particles called photons, key experiments on the wave properties of light were performed. For example, it was established that the color of visible light is associated with different wavelengths of light. Table 2.1 shows the range of wavelengths corresponding to different colors. The connection between optical and electrical phenomena was established by Maxwell in 1864. This extended the concept of light to include the complete electromagnetic spectrum. A great deal of effort was, and continues to be, spent gathering information on the behavior of light.