Quantum MechanicsPub Date : 2019-05-14DOI: 10.23943/princeton/9780691209821.003.0007
P. Peebles
{"title":"Scattering Theory","authors":"P. Peebles","doi":"10.23943/princeton/9780691209821.003.0007","DOIUrl":"https://doi.org/10.23943/princeton/9780691209821.003.0007","url":null,"abstract":"This chapter studies applications drawn from scattering theory. A powerful and commonly used way to explore the interaction between particles is to study the way they scatter off each other. In the scattering problems considered here, motions are non-relativistic and particles are conserved: two particles move together, interact, and then move apart again. It is assumed that the range of the interaction is finite, so when the particles are well separated they move freely. In a scattering experiment, one imagines that the particles approach each other as wave packets with fairly definite momenta and positions. The motion is initially free, because the particles are separated by great distances compared to the range of their interaction. As the wave packets move together, the particles interact through a potential V that is some function of the particle separation. The wave packets then move apart in a scattering pattern that is determined by the interaction potential. The chapter simplifies the partial wave analysis by concentrating on s-wave scattering; this allows an easy treatment of interesting effects such as resonances and absorption.","PeriodicalId":257994,"journal":{"name":"Quantum Mechanics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127833214","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}
Quantum MechanicsPub Date : 2019-05-14DOI: 10.23943/princeton/9780691209821.003.0001
P. Peebles
{"title":"Historical Development","authors":"P. Peebles","doi":"10.23943/princeton/9780691209821.003.0001","DOIUrl":"https://doi.org/10.23943/princeton/9780691209821.003.0001","url":null,"abstract":"This chapter presents the origins of quantum mechanics. The story of how people hit on the highly non-intuitive world picture of quantum mechanics, in which the physical state of a system is represented by an element in an abstract linear space and its observable properties by operators in the space, is fascinating and exceedingly complicated. The much greater change from the classical world picture of Newtonian mechanics and general relativity to the quantum world picture came in many steps taken by many people, often against the better judgment of participants. There are three major elements in the story. The first is the experimental evidence that the energy of an isolated system can only assume special discrete or quantized values. The second is the idea that the energy is proportional to the frequency of a wave function associated with the system. The third is the connection between the de Broglie relation and energy quantization through the mathematical result that a wave equation with fixed boundary conditions allows only discrete quantized values of the frequency of oscillation of the wave function (as in the fundamental and harmonics of the vibration of a violin string).","PeriodicalId":257994,"journal":{"name":"Quantum Mechanics","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134470464","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}
Quantum MechanicsPub Date : 2019-05-14DOI: 10.23943/princeton/9780691209821.003.0005
P. Peebles
{"title":"Perturbation Theory","authors":"P. Peebles","doi":"10.23943/princeton/9780691209821.003.0005","DOIUrl":"https://doi.org/10.23943/princeton/9780691209821.003.0005","url":null,"abstract":"This chapter examines applications drawn from perturbation theory. The main topic in perturbation theory is the energy and spontaneous decay rate of the 21-cm hyperfine line in atomic hydrogen. Before there were electronic computers, people had quite an accurate theoretical understanding of the energy levels in helium and more complicated systems. The trick was (and is) to find approximation schemes that treat unimportant parts of a physical system in quite crude approximations while reducing the interesting parts to a problem simple enough that it is feasible to compute but yet detailed enough to yield accurate results. The approximation methods in the chapter deal with the effects of small changes in the Hamiltonian, resulting for example from the application of a static or time variable electric or magnetic field. This may cause small changes in energy levels, and it may induce transitions among eigenstates of the original Hamiltonian.","PeriodicalId":257994,"journal":{"name":"Quantum Mechanics","volume":"176 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124033665","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}
{"title":"ABSTRACT LINEAR SPACE OF STATE VECTORS","authors":"P. Peebles","doi":"10.2307/j.ctvxrpxzs.6","DOIUrl":"https://doi.org/10.2307/j.ctvxrpxzs.6","url":null,"abstract":"This chapter discusses abstract linear space of state vectors. The wave mechanics presented in the previous chapter is easily generalized for use in all the applications of quantum mechanics explained in this book. In particular, to take account of spin, one just replaces the wave function with a set of functions, one for each possible choice of the quantum numbers of the z components of the spins of the particles. However, as the chapter shows, it is easy to adapt the wave mechanics formalism to the more general scheme that represents the states of a system as elements of an abstract linear space rather than a space of wave functions. This approach has the virtue that one can explicitly see the logic of the generalization of the wave function to take account of spin, and this is the road to other generalizations, like quantum field theory.","PeriodicalId":257994,"journal":{"name":"Quantum Mechanics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122394309","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}
Quantum MechanicsPub Date : 2019-05-14DOI: 10.23943/princeton/9780691209821.003.0006
P. Peebles
{"title":"Atomic and Molecular Structure","authors":"P. Peebles","doi":"10.23943/princeton/9780691209821.003.0006","DOIUrl":"https://doi.org/10.23943/princeton/9780691209821.003.0006","url":null,"abstract":"This chapter assesses some applications drawn from atomic and molecular structure. It deals with the structures of the lighter atoms and the simplest molecule, molecular hydrogen. The main approximation method used here is the energy variational principle, which is a powerful technique for computing the low-lying energies of a system such as an atom or molecule. The chapter then introduces the Pauli exclusion principle, which governs the symmetry of the state vector for a system of identical particles such as electrons. Two general features of the exclusion principle are worth noting. First, although the spins make only a very weak contribution to the Hamiltonians for helium, the lowest energy state with spin one is above the spin zero ground state, which is a considerable difference. Second, an electron arriving as a cosmic ray particle from a distant galaxy has to have a wave function antisymmetric with respect to the local electrons, even though the new electron has been away from us for a long time.","PeriodicalId":257994,"journal":{"name":"Quantum Mechanics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116946170","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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