دانلود کتاب دریچه اتم هیدروژن به فیزیک کوانتومی، تقارن‌ها و جابجایی تابشی آن

Understanding the hydrogen atom is at the heart of modern physics. Exploring the energy levels and the symmetry of the most fundamental twobody system has led to advances in atomic physics, quantum mechanics, quantum electrodynamics, and elementary particle physics. Regularities in the spectrum of atomic hydrogen inspired Bohr’s theory of the atom and what has been called the old quantum theory, which described general features of the atom but not detailed behavior. A crucial success of the Schrodinger theory of wave mechanics, which was introduced about 1921, was the calculation of the absorption and emission of radiation and the second and third order Stark effect in the H atom. This nonrelativistic theory had many successes but was unable to deal with the fine structure of the hydrogenic lines, a challenge solved by the relativistic Dirac theory, which explained the fine structure and gave a value for the spin component of the magnetic moment of the electron (g-2). Experiments by Lamb and Retherford in 1947 revealed problems with the Dirac theory, in particular that it incorrectly predicted that the 2s1/2 and 2p1/2 levels were degenerate. The method of renormalization was introduced by Bethe to compute the Lamb shift, paving the way for the computation of radiative effects due to the interaction of the electron with its own radiation field or with the quantum fluctuations of the electromagnetic field, while avoiding divergences. This was the birth of Quantum Electrodynamics (QED), today a mature theory that has predicted the energy levels of the hydrogen atom and the anomalous magnetic moment of the electron to unprecedented precision, the most precise physical theory in history [1, 2]. Today, significant effort has been focused on the calculation of higher-order radiative shifts. However, in this text, we focus on a deeper understanding of the H atom and the first-order radiative interaction that accounts for 96% of the shift. Measurement and explanation of the properties of the hydrogen atom have been central to the development of modern physics over the last century. One of the most useful and profound ways to understand its properties is through its symmetries, which we explore, beginning with the symmetry of the Hamiltonian, which reflects the symmetry of the degenerate levels, then the larger non-invariance and spectrum-generating groups, which include all the states. The successes in using symmetry to explore the hydrogen atom led to the use of symmetry to understand and model other physical systems, particularly elementary particles. In Part 1, we discuss the role of symmetry and group theory in understanding the H atom over the last century, and introduce some basic ideas about symmetry groups. We provide an integrated treatment of the symmetries of the classical and Schr¨odinger hydrogen atom, including the four-dimensional rotational symmetry group SO(4) (special orthogonal group in four dimensions), which is the degeneracy group, with the rotations in four dimensions generated by the angular momentum vector and Runge– Lenz vector, which points along the semi-major axis of the eliptical orbit. We calculate the energy levels using these symmetry operators and consider the wavefunctions in configuration space and in three- and four-dimensional momentum space, and how the wavefunctions are transformed by the generators.We introduce a novel set of wavefunctions that includes both the bound and scattering states and that uses the usual Schrodinger quantum numbers nlm. These wavefunctions allow for a simplified and integrated approach to quantum theory calculations. The semi-classical limit of the wavefunctions is explored.