49.1 Connecting quantum theories to experimental results
Our emphasis has been on the fundamental mathematical structures that occur in quantum theory, but using these to derive results that can be compared to real world experiments requires additional techniques. Such techniques are the main topics of typical standard physics textbooks dealing with quantum mechanics and quantum field theory. Among the most important are:
• Scattering theory. In the usual single-particle quantum mechanics, one can study solutions to the Schr¨odinger equation that in the far past and future correspond to free particle solutions, while interacting with a potential at some intermediate finite times. This corresponds to the situation analyzed experimentally through the study of scattering processes.
In quantum field theory one generalizes this to the case of “inelastic scattering”, where particles are being produced as well as scattered. Such calculations are of central importance in high energy physics, where most experimental results come from colliding accelerated particles and studying these sorts of scattering and particle production processes.
• Perturbation methods. Rarely can one find exact solutions to quantum mechanical problems, so one needs to have at hand an array of approximation techniques. The most important is perturbation theory, the study of how to construct series expansions about exact solutions. This technique can be applied to a wide variety of situations, as long as the system in question is not too dramatically of a diferent nature than one for which an exact solution exists. In practice this means that one studies in this manner Hamiltonians that consist of a quadratic term (and thus exactly solvable by the methods we have discussed) plus a higher-order term multiplied by a small parameter . Various methods are available to compute the terms in a power series solution of the theory about = 0, and such calculational methods are an important topic of most quantum mechanics and quantum field theory textbooks.
来源与版本
正文：英文 · OCR 机器稿 · 待校对
核对状态：OCR 机器稿 · 待校对
原书 PDF · 印刷页 530、531、532
来源版本：2025-10-20
来源 PDF SHA-256：5a1941b2443b54d5db3d055f1e5ba390429b7a728475258017aaac87ee85a837
OCR 来源 SHA-256：51bbfff54ace3ba6a45d54959a5ac3134b5c39546cc607baebb65f5925f254df
OCR 产物 SHA-256：51bbfff54ace3ba6a45d54959a5ac3134b5c39546cc607baebb65f5925f254df