In the early years of the twentieth century, Ernest Rutherford undertook pioneering studies of radioactive decay sequences. Kinetic molecular theory and the theory of radioactive decay both are based on statistical considerations. On the regularity-between-states view of causality, each stage of the decay process is in a cause-effect relation to its successor stage. The decay of thorium, qua ensemble of atoms, qualifies as a causal process on the regularity-between-states view. Regularities had been established that link the heating of elements and the occurrence of lines in their spectra. The causal relations at stake are regularities of transition between electron states, and to establish these regularities is to enable explanatory arguments to be given of atomic spectra. The correspondence principle provided a link between discontinuous transitions within the atom to continuous motions adequately described by classical physics. However, Neils Bohr's theory of the atom retained both quantum and classical aspects. Quantum mechanics and classical mechanics both feature causal laws.
In the early years of the twentieth century, Ernest Rutherford undertook pioneering studies of radioactive decay sequences. Kinetic molecular theory and the theory of radioactive decay both are based on statistical considerations. On the regularity-between-states view of causality, each stage of the decay process is in a cause-effect relation to its successor stage. The decay of thorium, qua ensemble of atoms, qualifies as a causal process on the regularity-between-states view. Regularities had been established that link the heating of elements and the occurrence of lines in their spectra. The causal relations at stake are regularities of transition between electron states, and to establish these regularities is to enable explanatory arguments to be given of atomic spectra. The correspondence principle provided a link between discontinuous transitions within the atom to continuous motions adequately described by classical physics. However, Neils Bohr's theory of the atom retained both quantum and classical aspects. Quantum mechanics and classical mechanics both feature causal laws.
P reliminary S urvey With the coming of the twentieth century, there came into being a new physics which was especially concerned with phenomena on the atomic and sub-atomic scale. It brought with it a new way of interpreting the phenomena of inanimate nature, which was destined in time to sweep away all the difficulties besetting the old classical mechanics. A preliminary glance over the vast territory of this new physics reveals three outstanding landmarks. First we notice an investigation which Prof. Planck of Berlin published in 1899. His aim was so to amend the classical mechanics that it should fit the observed facts of radiation, and show why the energy of bodies was not wholly transformed into radiation. We have already seen that this was likely to involve giving up either continuity or causality or the representation of phenomena as changes taking place in space and time. Actually his investigation seemed to show that continuity had to be given up, suggesting that in the last resort changes in the universe do not consist of continuous motions in space and time, but are in some way discontinuous. The classical mechanics had envisaged a world constructed of matter and radiation, the matter consisting of atoms and the radiation of waves. Planck's theory called for an atomicity of radiation similar to that which was so well established for matter.
1. Origins - Chapter One: Atoms Waves Quanta Before and after Democritus Titus Lucretius Carus Isaac Newton on atoms. Chapter Two: Spectra Ions Radiant matter Atoms, electrons, waves Discovery of spectral analysis The beginnings of television William Crookes Kinetic theory of gases Mikhail Vasilyevich Lomonosov. Chapter Three: The planetary atom Spectral series Photons Victory of atomistics The indivisible atom The diffraction grating Just what hath Rutherford wrought? Light pressure Chapter Four: Pre-Bohr times The Bohr atom Post-Bohr times Formal model of the atom Niels Henrik David Bohr Experimental proof of Bohr's postulates. Chapter Five: Teachings of the Ancients First attempts Elements and atoms Table of elements The Periodic law Atoms and people. 2. Ideas - Chapter Six: Contemporaries comment on Bohr's theory Phenomenon, image, concept, formula Heisenberg's matrix mechanics The foundation of physics. Chapter Seven: Louis de Broglie Matter waves Optical-mechanical analogy Schrodinger's wave mechanics The life of Boscovich ... ... and his atom Paul Ehrenfest (1880-1933). Chapter Eight: Schrodinger's equation The meaning of the psi function The image of the atom Quantum truth Compton's experiment Electron diffraction. Chapter Nine: Wave-particle duality Uncertainty relation Complementarity principle Duality and uncertainty Poets and the complementarity principle. Chapter Ten: Heads or tails and target shooting Electron diffraction Probability waves Electron waves The atom and probability Probability and atomic spectra Causality and chance, probability and certainty People, events, quanta. Chapter Eleven - What is an atom? What is quantum mechanics? Physical reality In search of the last concepts. 3. Results - Chapter Twelve: Wilhelm Konrad Rontgen Antoine Henri Becquerel Pierre and Marie Curie Ernest Rutherford and Frederick Soddy The energy of radium X-ray waves. Chapter Thirteen: The chemisty of radioelements Isotopes uranium family Stable isotopes Radioactive decay energy Nuclear binding energy Uranium Earth and radium Knights of the fifth decimal place. Chapter Fourteen: Probing into the nucleus The neutron Artificial radioactivity Slow neutrons Nuclear fission Letters about fission. Chapter Fifteen: Tunnel effect Effective cross-sections of reactions Neutron cross-sections Nuclear fission Labelled atoms Radiocarbon dating. Chapter Sixteen: Chain reaction Nuclear reactor Spontaneous fission of uranium The natural nuclear reactor at Oklo. Chapter Seventeen: Atomic Energy Plutonium The atomic bomb The atomic problem A chronology of the atomic era Soddy on atomic energy. Chapter Eighteen: Solar light Crucibles of elements The fate of the Sun The Sun, life and chlorophyll Life under the Sun A sun on earth Quanta around us. 4. Reflections - Chapter Nineteen: Inception of the scientific method Essence of the scientific method and its development. Truth and completeness of the scientific picture of the world. Science and humanity Boundaries of the scientific method Science and art Future of science Epilogue.
Something is rotten in the state of Denmark. Shakespeare , Hamlet, Act 1 Scene 4 The rise and fall of the old quantum theory The principles of the old quantum theory were first articulated by Niels Bohr in 1913 in a three-part paper titled “On the Constitution of Atoms and Molecules.” Bohr had adopted Ernest Rutherford's model of the atom, according to which the mass of the atom is concentrated in a small central nucleus, while the electrons orbit the nucleus in planetary trajectories. The key challenge facing Rutherford's model was that it was unstable: according to classical electrodynamics, the electron, which is a moving charged body, should radiate energy and so eventually collapse into the nucleus. Bohr's solution was to incorporate Max Planck's theory of radiation, according to which “the energy radiation from an atomic system does not take place in the continuous way assumed in ordinary electrodynamics, but that it, on the contrary, takes place in distinctly separated emissions” (Bohr 1913, p. 4; BCW 2, p. 164). In this early paper, and most subsequent accounts, Bohr summarized his quantum theory by means of two assumptions or postulates. According to the first postulate, electrons cannot travel in any path they like around the nucleus, rather atomic systems can only exist in a series of discrete “stationary states,” in which the electron is in a particular allowed stable periodic orbit and is not emitting radiation.
Most textbooks say that quantum mechanics came into being when Max Planck, in a desperate attempt to construct a theory that explained experimental data, explored the radical idea of energy being radiated or absorbed by all bodies in discrete packets (or quanta). The energy content of a quantum of radiation is proportional to the frequency of the radiation emitted or absorbed, as in , and the proportionality constant bears the name of Planck. Planck himself was rather uncomfortable with the idea of energy packets, and spent a considerable amount of time in later years trying to “restore” the classical picture of continuous energy exchange between bodies and surroundings. However, in 1905 Einstein was able to use the idea of the quantum to explain the mechanism of the photoelectric effect, which cannot be explained in any other way! This established the reality of the quantum and so, it may be said that Einstein, rather than Planck, is the father of quantum mechanics. Within a few years, Neils Bohr constructed his model of the hydrogen atom in which the electron can only occupy certain special orbits around the nucleus, and any jump between these orbits is accompanied by energy being absorbed or emitted in the form of quanta. The nearly exact agreement of Bohr’s predictions based on the model and observed hydrogen atomic spectra was among the first impressive accomplishments of quantum mechanics.
Why yet another book on quantum mechanics? Quantum mechanics was born in the first quarter of the twentieth century and has received an enormous number of theoretical and experimental confirmations over the years. It is considered to be the fundamental physical paradigm, and has a wide range of applications, from cosmology to chemistry, and from biology to information sciences. It is one of the greatest intellectual achievements of the past century. As an effect of its invention, the very concept of physical reality was changed, and “observation,” “measurement,” “prediction,” and “state of the system” acquired a new and deeper meaning. Probability was not unknown in physics: it was introduced by Boltzmann in order to control the behavior of a system with a very large number of particles. It was the missing concept in order to understand the thermodynamics of macroscopic bodies, but the structure of the physical laws remained still deterministic. The introduction of probability was needed as a consequence of our lack of knowledge of the initial conditions of the system and of our inability to solve an enormous number of coupled non-linear differential equations. In quantum mechanics, the tune is different: if we have 10 6 radioactive atoms no intrinsic unknown variables decide which of them will decay first. What we observe experimentally seems to be an irreducible random process. The original explanation of this phenomenon in quantum mechanics was rather unexpected.
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.