Quantum mechanics is essentially a 20th century development that is based on a number of observations that defied classical explanations. While some of these experiments have semiclassical explanations, the triumph of quantum mechanics is that it gives precise verification for an overwhelming number of experimental observations. Its extensions into relativistic quantum mechanics through quantum electrodynamics (QED), electro-weak theory, and quantum chromodynamics (QCD) have led us to the Standard Model of today. While the number of unanswered questions remains approximately constant at each stage of development, the number of answered questions that relate theory with experiment continues to grow rapidly. In this chapter, some of the historical landmarks in the development of the theory are noted. The resolution of the dilemmas presented by classical theory will be dealt with in later chapters, but these are listed to motivate the break from classical mechanics. Because of the apparently unphysical nature of the postulates upon which quantum mechanics is founded, we supply motivation and justification for this break. In the first part of this chapter, we will review some of the experiments that confounded classical theory, and then introduce a formalism that provides some rationale for the postulates upon which quantum mechanics is based. In the end, these postulates will stand on their own.
Quantum mechanics is essentially a 20th century development that is based on a number of observations that defied classical explanations. While some of these experiments have semiclassical explanations, the triumph of quantum mechanics is that it gives precise verification for an overwhelming number of experimental observations. Its extensions into relativistic quantum mechanics through quantum electrodynamics (QED), electro-weak theory, and quantum chromodynamics (QCD) have led us to the Standard Model of today. While the number of unanswered questions remains approximately constant at each stage of development, the number of answered questions that relate theory with experiment continues to grow rapidly. In this chapter, some of the historical landmarks in the development of the theory are noted. The resolution of the dilemmas presented by classical theory will be dealt with in later chapters, but these are listed to motivate the break from classical mechanics. Because of the apparently unphysical nature of the postulates upon which quantum mechanics is founded, we supply motivation and justification for this break. In the first part of this chapter, we will review some of the experiments that confounded classical theory, and then introduce a formalism that provides some rationale for the postulates upon which quantum mechanics is based. In the end, these postulates will stand on their own.
This chapter introduces two approaches to quantum mechanics, one is to follow the historical development of the theory from the first indications that the whole fabric of classical mechanics and electrodynamics should be held in doubt to the resolution of the problem. The other approach is to stand back at a point late in the development of the theory and see its underlying theoretical structure. The chapter shows that in the first approach the theory is seen gradually emerging from confusion and dilemma, while the second is a more formal approach that can still be exciting and compelling in a different sense. The chapter highlights the logic and elegance in a scheme that starts from only a few postulates, yet reveals a rich, experimentally verifiable structure. It traces some of the most fundamental concepts of the nature of matter and its behaviour that were overthrown and replaced by a puzzling but powerful new description.
Abstract Following the path by which humanity learned quantum mechanics can lead to an improved understanding of the theory and the origins of its perceived limitations. Our goal is to retrace the development by investigating primary sources, including original published papers and letters, with attention to their timing and influence. Quantum mechanics began in 1900 with the introduction of Planck’s constant, which lead to the “old” quantum theory and Bohr’s model of the atom. With the introduction of matter waves in 1924, a second more intense period began. By 1928 the complete fundamental structure of quantum mechanics was established with the introduction of the Schrödinger equation, the proof of its equivalence to Heisenberg’s matrix mechanics, and the introduction of the relativistic Dirac equation. The theory retains the same essential form today, fueling the technological revolution that began in the last century. We culminate with an introduction to quantum information and computing. This completely new physical scientific paradigm was developed largely in Germany during a period of enormous social, economic, and political upheaval—in a hostile intellectual environment—that parallels the overturning of classical physics. It is striking that all the problems debated today were immediately recognized by the founders of the theory and instructive to see how they dealt with the various issues. We emphasize the centrality of the often neglected second quantization form of the theory for questions of interpretation and give a detailed examination of von Neumann’s widely misunderstood hidden variable theorem.
In this chapter we review the ideas and discoveries that lead to the development of quantum mechanics. Like other theories in physics, it was motivated by a series of experimental results that were at odds with the prevailing theories of the time. New concepts were introduced to explain those experiments, which in turn led to new experiments and more discoveries. Quantum mechanics took its current shape about 100 years ago and continues to provide a formidable framework for describing not only natural phenomena but also for leading us to new technologies, such as quantum information processing.
This chapter starts with the historical development of quantum mechanics and explanations of key concepts behind fundamental discoveries such as Planck's hypothesis, the photoelectric effect, Bohr's atomic model, Compton scattering, the de Broglie hypothesis, the Pauli exclusion principle, the Schrödinger equation, Heisenberg quantum mechanics and the uncertainty principle, the Born interpretation of wave function, the Davisson and Germer experiment, and Dirac relativistic quantum mechanics, which made important contributions to the foundation of modern quantum mechanics. Concepts like the particle properties of radiation, the wave properties of matter, quantized energy and momentum, and the idea that one can no longer know exactly where a single particle like an electron is at any instant of time are brought out clearly through this chapter. A list of important quantum mechanical parameters along with solved examples and unsolved exercises on the key concepts are included towards the end.
By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems. Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing. Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory. The photoelectric effect and photons In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.
The behavior of classical macroscopic particles – from baseballs to planets – is governed by Newtonian mechanics as we have described in the first chapters of this book. The behavior of very small particles, on the other hand, is governed by an entirely different collection of equations and rules that go under the name of “quantum mechanics” and these particles are referred to as quantum particles. These rules have analogies to classical mechanics, but are fundamentally different and somewhat mysterious as we discussed in Chapter 8. The fundamental principles of quantum mechanics cannot be proven to be correct. They were developed based on the results of experimental observation, by analogy with classical mechanics, and through the consideration of logical implications of the formalisms used. There is no way to derive the fundamental elements of quantum mechanics, any more than one could predict from first principles that Newtonian forces should add as vectors. On the other hand, quantum mechanics is among the most rigorously tested theories in science, and the predictions of quantum mechanics have, so far, always been in agreement with experiment. In this chapter, we will present quantum mechanics as a series of postulates and examine their implications in application to simple one-dimensional systems. In the next chapter we will examine quantum effects in real systems including atoms, molecules, crystals, and artificially engineered nano-structures. Postulates of quantum mechanics QM Postulate 1: A quantum particle is described by a wave function Ψ( x , y , z , t ) which is a function of spatial coordinates and time. All physically determinable quantities can be derived from the wave function Ψ( x , y , z , t ) ; quantities which cannot be found from the wave function are not physically meaningful. Note that some things that one could ask about a quantum particle, for example the exact position and simultaneous exact momentum of a particle, are not derivable from the wave function and are therefore considered indeterminate (or uncertain ). These are things which cannot ever be known about a particle, and, as such, they are meaningless to contemplate.