To date, the physical theory that most accurately describes the behavior of the atomic world is quantum mechanics. Since spectroscopy uses light to probe the atomic and molecular world, it should not be much of a surprise to learn that quantum mechanics is used to describe how spectroscopy works. Nobel Prize-winning physicist Richard Feynmann once said, "If you think you understand quantum mechanics, you don't understand quantum mechanics." This chapter won't bring you to a complete understanding of quantum mechanics, Feynmann's quote notwithstanding. But it will try to point out the important aspects, and hopefully it will at least leave the reader with the understanding that spectroscopy is quantum-mechanically based. Science's job is to try to understand the natural universe. To do this, scientists try to generate models to describe and predict the universe's behavior. (Not the behavior of the entire universe, but small selected parts of it.) If the model and the universe do not agree, there are two choices: change the model, or change the universe. Since all attempts at changing the universe have failed, our only choice is to change the model. Since the 1600s, scientific advance has accelerated at least in part because the proposed models of the universe have been increasingly more acceptable. Perhaps the first true âscientificâ investigation (by the modern definition) was Robert Boyle's investigation of gases in the 1660s. While there were some noteworthy incorrect or improper models developed (phlogiston and vitalism are two that come to mind immediately, but doubtless there are others), incorrect or improper models were ultimately replaced by more viable models. One such group of models was what we now call Newton's laws of motion. In just a few statements, verbal or mathematical, Newton's laws accurately describe the motion of matter. Further, these models withstood the test of multiple examinations, and are accepted as proper models of how matter behaves.
To date, the physical theory that most accurately describes the behavior of the atomic world is quantum mechanics. Since spectroscopy uses light to probe the atomic and molecular world, it should not be much of a surprise to learn that quantum mechanics is used to describe how spectroscopy works. Nobel Prize-winning physicist Richard Feynmann once said, "If you think you understand quantum mechanics, you don't understand quantum mechanics." This chapter won't bring you to a complete understanding of quantum mechanics, Feynmann's quote notwithstanding. But it will try to point out the important aspects, and hopefully it will at least leave the reader with the understanding that spectroscopy is quantum-mechanically based. Science's job is to try to understand the natural universe. To do this, scientists try to generate models to describe and predict the universe's behavior. (Not the behavior of the entire universe, but small selected parts of it.) If the model and the universe do not agree, there are two choices: change the model, or change the universe. Since all attempts at changing the universe have failed, our only choice is to change the model. Since the 1600s, scientific advance has accelerated at least in part because the proposed models of the universe have been increasingly more acceptable. Perhaps the first true âscientificâ investigation (by the modern definition) was Robert Boyle's investigation of gases in the 1660s. While there were some noteworthy incorrect or improper models developed (phlogiston and vitalism are two that come to mind immediately, but doubtless there are others), incorrect or improper models were ultimately replaced by more viable models. One such group of models was what we now call Newton's laws of motion. In just a few statements, verbal or mathematical, Newton's laws accurately describe the motion of matter. Further, these models withstood the test of multiple examinations, and are accepted as proper models of how matter behaves.
The objective of this chapter is to go over a few of the basic concepts of quantum mechanics in preparation for a discussion of spectroscopy, which is in many ways the business end of quantum mechanics, at least for chemical scientists. We will also need a few quantum mechanical ideas from time to time in our study of thermodynamics and of kinetics. Why should we learn quantum mechanics at all? Atoms and molecules are small, and their constituent parts, electrons, protons and neutrons, are even smaller. Early in the twentieth century, we learned that small things don't obey the laws of classical mechanics. A different kind of mechanics, quantum mechanics, is required to understand chemistry on a fundamental level. In fact, we need different mechanical theories to treat extremes of both size and speed. Figure 2.1 summarizes the situation. There isn't a sharp cut-off between the various sectors of this diagram. Also note that some of the theories are more general than others. We could in principle use quantum mechanics or general relativity to predict the trajectories of tennis balls, but it just isn't worth the effort, given that classical mechanics works perfectly well in this range of masses and speeds. On the other hand, classical mechanics doesn't give very good results for things that are either extremely large, or small, or fast. Like it or not, to discuss phenomena on an atomic scale, we need quantum mechanics. Ordinary (non-relativistic) quantum mechanics is generally adequate, although electrons in heavy atoms sometimes reach relativistic speeds (approaching the speed of light, c ), requiring relativistic quantum mechanics.
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.
The Quantum theory deals with the microscopic structure of the Universe that describes the finer details of nature at the subatomic domain.To a physicist, quantum mechanics is one of the three great pillars supporting our intuition of evocative, bewildering and fascinating natural World as we continuously struggle with the inescapable strangeness of the subatomic domain as if something strange is always afoot.It is well accepted fact that quantum mechanics is a physical theory that describes the way things behave at subatomic level which is quite dazzling in its precision and explanatory power.A test of quantum electrodynamics, the oldest and best understood of the modern quantum theory that involves measuring the way an electron behaves in the vicinity of a magnetic force. Many of the technological and social changes that have revolutionized our lives have actually risen out of the fundamental theoretical research carried out with only motivation to understand the World in a better way than ever. For example, the invention of transistor actually came with the fundamental theoretical research on the Uncertainty Principle which states that the uncertainty of the position of a particle times the uncertainty of its velocity is always a constant. If we double the certainty of the position of the particle, we have to make half the certainty of its velocity and vice versa. Quantum theory is perhaps the prime example of the infinitely esoteric in the sense that it describes a World in which a particle really can be in several places at once and it moves from one place to another by exploring the entire Universe simultaneously-the theory of simultaneity. The diverse and complex Universe is actually made of a few tiny particles according to the rules of quantum theory which is so simple that can be summarized on the back of an envelope. The more we understand about the elemental nature of the Universe, the simpler it looks. We have already discovered that everything in the diverse and complex Universe is nothing but the different assemblies of atoms, and the wide variety of atoms are constructed using the three building blocks at the sub-atomic domain i.e. subatomic particles: protons, neutrons and electrons. We have also discovered that protons and neutrons ate made up of combination of three entities called quarks. And that is where things stop as far as recent discovery is concerned. But the recent progress in particle physics inspiring the quest for the ultimate unified theory of physics that can describe everything in the Universe in one go. The discovery of Boson particle certainty will revolutionaries the Newton's mass concept and gravity into whole new looks. To an optimistic point of view, we must hope the best out of the progress in physics.
Dad I understand that light is emitted when an atom decays from an excited state to a lower energy state. Feynman That's right. Dad And light consists of particles called photons. Feynman Yes. Dad So the photon ‘particle’ must be inside the atom when it is in the excited state. Feynman Well no. Dad Well how do you explain that the photon comes out of the atom when it was not there in the first place. Feynman (Physics Teacher 1969) I'm sorry. I don't know I can't explain it to you. INTRODUCTION As was stated in Chapter 1, spectroscopy is a study of the interaction of matter with radiation. In order to understand their mutual interaction, we must therefore characterize both radiation and matter. The starting point is quantum mechanics, because the origin of quantum mechanics was based on unexplained phenomena related to both the nature of electromagnetic radiation and that of matter. In fact, quantum mechanics owes its birth to some puzzling results of spectral and other experiments. We may say that “spectroscopy is quantum mechanics in action.” We therefore begin our study of quantum mechanics with a recapitulation of its postulates. An understanding of the postulates is also essential for our development of the time-dependent perturbation theory and also forms the basis for the connection between theory and experiment. Indeed, spectroscopy is the experimental verification of the laws of quantum mechanics. Quantum mechanics is based on a few postulates (from the Latin postulatum ), meaning a truth that does not need any further proof, because it is obvious by itself, and its success lies in the fact that no experiment till date has proved it wrong. There is no agreement of how many axioms one needs to describe the machinery of quantum mechanics; however, the six given below is an acceptable number.
What is usually called modern physics is based on two theories: relativity, which we have just nished discussing, and quantum mechanics (also called quantum theory). While some of the ideas of relativity, such as time dilation and length contraction, at rst seemed rather strange, we saw that they followed logically from the two postulates of relativity. We will see below that the ideas of quantum mechanics are also strange. Most physicists would agree that they are much stranger than relativity. In fact, we will see that there are no satisfactory explanations. To quote two Nobel Prize laureates, Murray Gell-Mann and Richard Feynman, “Nobody really understands quantum theory.” Despite this, it is one of the best-tested theories that we have. In some cases, the agreement between the theoretical prediction and experiment is better than 1 part in a million. There are many useful devices that are based on quantum mechanics. They include anything that uses microelectronics, such as a cell phone, DVD player, or computer, nuclear reactors, and medical imaging devices such as MRI and PET.
Quantum Mechanics is an essential topic in today's physics curriculum at both the undergraduate and graduate levels. Quantum mechanics can explain the microscopic world with fantastic accuracy; the fruits from its insights have created technologies that have revolutionized the world. Computers, lasers, mobile telephones, optical communications are but a few examples. The language of quantum mechanics is now an accepted part of the language of physics and day-to-day usage of this language provides physicists with the intuition that is essential for achieving meaningful results. Nevertheless, most physicists acknowledge that, at least once in their scientific career, they have had difficulties understanding the foundations of quantum theory, perhaps even the impression that a really satisfactory and convincing formulation of the theory is still lacking. Numerous quantum mechanics textbooks are available for explaining quantum formalism and applying it to understand problems such as the properties of atoms, molecules, liquids, and solids; the interactions between matter and radiation; and more generally to understand the physical world that surrounds us. Other texts are available for elucidating the historical development of this discipline and describing the steps through which it went before quantum mechanics reached its modern formulation. In contrast, books are rare that review the conceptual difficulties of the theory and then provide a comprehensive overview of the various attempts to reformulate quantum mechanics in order to solve these difficulties. The present text by Franck Laloë does precisely this.