Pub Date : 2020-05-07DOI: 10.1093/oso/9780198854227.003.0017
M. Zubairy
In this chapter, the Schrödinger equation is “derived” for particles that can be described by de Broglie waves. The Schrödinger equation is very different from the corresponding equation of motion in classical mechanics. In order to illustrate the fundamental differences between the two theories, one of the simplest problems of particle dynamics is solved in both Newtonian and quantum mechanics. This simple example also helps to show that quantum mechanics is the fundamental theory and classical mechanics is an approximation, a remarkably good approximation, when considering macroscopic objects. The solution of the Schrödinger equation is presented for a particle inside a box and the quantization condition is derived. The amazing possibility of quantum tunneling when a particle is incident on a barrier of height larger than the energy of the incident particle is also discussed. Finally the three-dimensional Schrödinger equation is solved for the hydrogen atom.
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Pub Date : 2020-05-07DOI: 10.1093/oso/9780198854227.003.0002
M. Zubairy
In the spirit of making this book reasonably self-contained, certain topics that may be required in understanding the foundation and the applications of quantum mechanics are discussed. Foremost are the definition and properties of the complex numbers, such as De Moivre’s theorem and Euler’s identity. Trigonometry and vector analysis are the necessary topics for almost any discussion of physical phenomena. In this chapter these topics are discussed to the extent that makes their use in subsequent chapters quite natural and normal. Another topic that reverberates throughout this book due to the nature of quantum mechanics is probability theory. Here the main ideas of probability theory are presented that should be sufficient for an understanding of the topics discussed in this book.
{"title":"Mathematical Background","authors":"M. Zubairy","doi":"10.1093/oso/9780198854227.003.0002","DOIUrl":"https://doi.org/10.1093/oso/9780198854227.003.0002","url":null,"abstract":"In the spirit of making this book reasonably self-contained, certain topics that may be required in understanding the foundation and the applications of quantum mechanics are discussed. Foremost are the definition and properties of the complex numbers, such as De Moivre’s theorem and Euler’s identity. Trigonometry and vector analysis are the necessary topics for almost any discussion of physical phenomena. In this chapter these topics are discussed to the extent that makes their use in subsequent chapters quite natural and normal. Another topic that reverberates throughout this book due to the nature of quantum mechanics is probability theory. Here the main ideas of probability theory are presented that should be sufficient for an understanding of the topics discussed in this book.","PeriodicalId":175266,"journal":{"name":"Quantum Mechanics for Beginners","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127198438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-07DOI: 10.1093/oso/9780198854227.003.0005
M. Zubairy
The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.
{"title":"Fundamentals of Quantum Mechanics","authors":"M. Zubairy","doi":"10.1093/oso/9780198854227.003.0005","DOIUrl":"https://doi.org/10.1093/oso/9780198854227.003.0005","url":null,"abstract":"The laws of quantum mechanics were formulated in the year 1925 through the work of Werner Heisenberg, followed by Max Born, Pascual Jordan, Paul Dirac, and Wolfgang Pauli. A separate but equivalent approach was independently developed by Erwin Schrödinger in early 1926. The laws governing quantum mechanics were highly mathematical and their aim was to explain many unresolved problems within the framework of a formal theory. The conceptual foundation emerged in the subsequent 2–3 years that indicated how radically different the new laws were from classical physics. In this chapter some of these salient features of quantum mechanics are discussed. The topics include the quantization of energy, wave–particle duality, the probabilistic nature of quantum mechanics, Heisenberg uncertainty relations, Bohr’s principle of complementarity, and quantum superposition and entanglement. This discussion should indicate how different and counterintuitive its fundamentals are from those of classical physics.","PeriodicalId":175266,"journal":{"name":"Quantum Mechanics for Beginners","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115356382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-07DOI: 10.1093/oso/9780198854227.003.0001
M. Zubairy
This chapter begins with a brief history of how classical mechanics evolved into quantum mechanics. Next a bird’s-eye view of the basic aspects of quantum mechanics and its applications is given. In subsequent chapters, these topics are discussed with reasonable completeness, with a minimum of mathematical background.
{"title":"What is this Book About?","authors":"M. Zubairy","doi":"10.1093/oso/9780198854227.003.0001","DOIUrl":"https://doi.org/10.1093/oso/9780198854227.003.0001","url":null,"abstract":"This chapter begins with a brief history of how classical mechanics evolved into quantum mechanics. Next a bird’s-eye view of the basic aspects of quantum mechanics and its applications is given. In subsequent chapters, these topics are discussed with reasonable completeness, with a minimum of mathematical background.","PeriodicalId":175266,"journal":{"name":"Quantum Mechanics for Beginners","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117143796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-07DOI: 10.1093/oso/9780198854227.003.0003
M. Zubairy
In Newtonian mechanics, a particle is described as an object that is characterized by certain properties. The most important characteristics of a particle are its mass, position, velocity, and acceleration. In this chapter, it is shown how a particle follows a well defined classical trajectory. The main characteristics of the dynamics of particles such as linear and angular momentum, force, energy, moment of inertia, and torque are presented. An understanding of these effects is essential in understanding and appreciating the laws of quantum mechanics. As an example of the Newtonian mechanics, the motion of an electron in electric and magnetic fields experiencing Lorentz force is discussed. This example explains how Thomson discovered the electron in the late nineteenth century.
{"title":"Particle Dynamics","authors":"M. Zubairy","doi":"10.1093/oso/9780198854227.003.0003","DOIUrl":"https://doi.org/10.1093/oso/9780198854227.003.0003","url":null,"abstract":"In Newtonian mechanics, a particle is described as an object that is characterized by certain properties. The most important characteristics of a particle are its mass, position, velocity, and acceleration. In this chapter, it is shown how a particle follows a well defined classical trajectory. The main characteristics of the dynamics of particles such as linear and angular momentum, force, energy, moment of inertia, and torque are presented. An understanding of these effects is essential in understanding and appreciating the laws of quantum mechanics. As an example of the Newtonian mechanics, the motion of an electron in electric and magnetic fields experiencing Lorentz force is discussed. This example explains how Thomson discovered the electron in the late nineteenth century.","PeriodicalId":175266,"journal":{"name":"Quantum Mechanics for Beginners","volume":"656 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134197686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-07DOI: 10.1093/oso/9780198854227.003.0004
M. Zubairy
One of the earliest and most important tenets of quantum mechanics is the wave-particle duality: light behaves sometimes like a wave and at other times as particle and similarly an electron can also behave both like a particle and as a wave. When the formal laws of quantum mechanics are formulated, the central quantity that describes the particles is the wave function. This points to the need for a good understanding of the properties of the waves. This chapter introduces the concepts and most essential applications that are required to follow the discussion of quantum mechanical laws and systems. The basic characteristics of the waves, such as the superposition principle are presented, and the interference and the diffraction phenomena are discussed. The Young’s double slit experiment in analysed and the formation of interference pattern is explicitly shown. The Rayleigh criterion for the microscopic resolution is also derived.
{"title":"Wave Theory","authors":"M. Zubairy","doi":"10.1093/oso/9780198854227.003.0004","DOIUrl":"https://doi.org/10.1093/oso/9780198854227.003.0004","url":null,"abstract":"One of the earliest and most important tenets of quantum mechanics is the wave-particle duality: light behaves sometimes like a wave and at other times as particle and similarly an electron can also behave both like a particle and as a wave. When the formal laws of quantum mechanics are formulated, the central quantity that describes the particles is the wave function. This points to the need for a good understanding of the properties of the waves. This chapter introduces the concepts and most essential applications that are required to follow the discussion of quantum mechanical laws and systems. The basic characteristics of the waves, such as the superposition principle are presented, and the interference and the diffraction phenomena are discussed. The Young’s double slit experiment in analysed and the formation of interference pattern is explicitly shown. The Rayleigh criterion for the microscopic resolution is also derived.","PeriodicalId":175266,"journal":{"name":"Quantum Mechanics for Beginners","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125226535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
It has always been a self-evident and obvious feature of any kind of communication that there should be an exchange of objects like photons or electrons between the sender and the receiver to convey any information. In this chapter a protocol is presented in which information is transmitted between a sender and receiver with no particles in the transmission channel. The basic building block of this counterfactual communication protocol, the Mach–Zehnder interferometer, is discussed. The concept of interaction-free measurement is also introduced.
{"title":"Optical Communication with Invisible Photons","authors":"Suhail Zubairy","doi":"10.1364/QIM.2013.T4B.1","DOIUrl":"https://doi.org/10.1364/QIM.2013.T4B.1","url":null,"abstract":"It has always been a self-evident and obvious feature of any kind of communication that there should be an exchange of objects like photons or electrons between the sender and the receiver to convey any information. In this chapter a protocol is presented in which information is transmitted between a sender and receiver with no particles in the transmission channel. The basic building block of this counterfactual communication protocol, the Mach–Zehnder interferometer, is discussed. The concept of interaction-free measurement is also introduced.","PeriodicalId":175266,"journal":{"name":"Quantum Mechanics for Beginners","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126435609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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