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Unformatted text preview: Phys 852, Quantum mechanics II, Spring 2009 Time-Independent Perturbation Theory Prof. Michael G. Moore, Michigan State University Atomic Physics Applications 1 Introduction For many reasons it is important to understand the basic level-structure of atomic hydrogen. As the simplest atom, it is a good starting point to understand the various mechanisms at work inside atoms. Early atomic physics was focussed on measuring and explaining the various atomic spectra. In recent years, atomic physics has progressed into new areas such as precision measurement, quantum optics, and even quantum computation. Atomic level structure still plays an important role in modern atomic physics, however, particularly in the rapidly evolving field of laser-cooled and trapped atoms. In solid-state physics, the atomic properties of impurity and dopant atoms play a major role, and the properties of quantum dots (artificial atoms) closely mirror those of real atoms. In nuclear physics, precision atomic spectroscopy allows precise measurements of isotopic masses and other isotopic properties. In addition, as the most abundant element, much astronomical data is based on measuring the spectral lines of hydrogen. Lastly, hydrogen is a system with many degeneracies, in which physically important results can be obtained from low-order degenerate perturbation theory, so it is an excellent area to practice applying what we have learned. We only have time to touch on atomic physics in this course, and we will focus only on the hydrogen atom for the time-being. This ignores the important and rich problem of electron-electron interaction, which dominates most of the periodic table of elements. The results from studying hydrogen, however, are readily generalized to other alkali metal (group I) atoms such as lithium (LI), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and Francium (Fr). Because their optical properties are governed by the behavior of a single valence electron, they are currently the predominant elements used in laser- cooling and trapping experiments, and all but Francium have been evaporatively cooled into Bose-Einstein condensates, which are many-body states with a single macroscopic wavefunction analogous to laser-light, but with bosonic atomic isotopes taking the place of photons. Singly ionized group II elements (Be, Mg, Ca,, Sr, Ba, Ra) are also hydrogen-like, and due to their similar optical properties, are commonly used in trapped-ion experiments, such as trapped-ion quantum computers. Lastly, exotic states such as positronium (electron-positron bound state) and muonic hydrogen (proton-muon bound state) also share the hydrogen level structure. In this section we will consider four basic effects, two based on the response of hydrogen to external fields, and two based based on internal effects related to the intrinsic spin of the electron and proton. These four effects are 1. DC Stark Effect : response of an atom to an applied static electric field....
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- Fall '08