Inversion of Gamow's Formula and Inverse Scattering

We present a pedagogical description of the inversion of Gamow's tunnelling formula and we compare it with the corresponding classical problem. We also discuss the issue of uniqueness in the solution and the result is compared with that obtained by the method of Gel'fand and Levitan. We hope that the article will be a valuable source to students who have studied classical mechanics and have some familiarity with quantum mechanics.Comment: LaTeX, 6 figurs in eps format. New abstract; notation in last equation has been correcte

Inversion of Gamow\u27s formula and inverse scattering

Gamow\u27s tunneling formula is inverted and the issue of the uniqueness of the solution is compared with the solution obtained by the method of Gel\u27fand and Levitan. Some insight is gained into the key differences between classical and quantum inverse scattering, which account for the fact that a potential can be uniquely determined in the latter but only to within a symmetry family in the former. (C) 2006 American Association of Physics Teachers

Probing The Cosmic Microwave Background Radiation With Actpol: A Millimeter-Wavelength, Polarization-Sensitive Receiver For The Atacama Cosmology Telescope

In this dissertation manuscript, we document the design, development, characterization, and scientific application of next-generation millimeter wavelength imaging technologies, conducted under the auspices of a NASA Space Technology Research Fellowship (NSTRF-11) grant, based at the University of Pennsylvania and completed under the advisement of Professor Mark J. Devlin. NASA’s Science Mission Directorate, supported by recommendations from the National Research Council (NRC) Decadal Survey, has placed the development of mission-enabling technologies for future-generation, seminal orbital platforms probing the nature of the early universe and cosmic inflation at the forefront of directives in space technology research. To work toward the rapid achievement of these directives, we highlight considerations for the design and integration of ACTPol, a new receiver for the Atacama Cosmology Telescope (ACT), capable of making millimeter-wavelength, polarization-sensitive observations of the Cosmic Microwave Background (CMB) at arcminute angular scales. ACT is a six-meter telescope located in northern Chile, dedicated to enhancing our understanding of the structure and evolution of the early universe by direct measurement of the CMB. We will focus first on the manner by which the integrated millimeter-wavelength imaging technologies of ACTPol with critical upgrades deployed to the ACT telescope superstructure and site, will enable the instrument to address a myriad of high-priority topics in experimental cosmology. We will then consider the design of the first ACTPol 150 GHz detector array package, which, along with a second 150 GHz array package and a multichroic array package with simultaneous 90 GHz and 150 GHz sensitivity, and associated optomechanical subsystems, comprises the ACTPol focal plane and, ultimately, receiver. Each of these detector array packages reside behind a set of normal-incidence, high-purity silicon reimaging optics with a novel anti-reflective coating geometry, the development flow of which will be detailed. As a root design system, the 150 GHz polarimeter array package consists of 1044 transition-edge sensor (TES) bolometers used to measure the response of 522 feedhorn-coupled polarimeters, which enable characterization of the linear orthogonal polarization of incident CMB radiation. The polarimeters are arranged in three hexagonal and three semi-hexagonal silicon wafer stacks, mechanically coupled to an octakaidecagonal, monolithic corrugated silicon feedhorn array (~140 mm diameter). Readout of the TES polarimeters is achieved using time-division SQUID multiplexing (TDM). The three polarimeter array packages comprising the ACTPol focal plane, and associated optical and cryomechanical elements of the fully integrated ACTPol receiver are cooled via a custom-designed, field-deployable dilution refrigerator (DR) providing a 100 mK bath temperature to the detectors, which have a target Tc of 150 mK. Given the unique cryomechanical constraints associated with this large-scale monolithic superconducting focal plane, we address the design considerations necessary for integration with the optical and cryogenic elements of the ACTPol receiver. The ACTPol receiver deployment and early operational protocol development are highlighted, and receiver laboratory and on-site operational optical, cryogenic, and detector performance characterization is considered. ACTPol early scientific operational results are then detailed, including CMB polarization measurements between l=200 and l=9000, measurements of galaxy clusters via the Sunyaev-Zel`dovich effect, and the first set of maps and associated analysis of ACTPol first season galactic field observations. Consideration is also given to work underway toward the realization of Advanced ACTPol, a next-generation receiver for ACT, with the enhanced capability to measure large-angular-scale regimes to probe inflationary cosmology. Finally, an outlook is provided in which lessons-learned from the development of a distributed portfolio of ACTPol and Advanced ACTPol receiver technologies will impact the realization of both near-term global-scale development efforts in experimental cosmology, including the CMB Stage-IV program, and, ultimately, a future-generation seminal CMB inflationary probe satellite platform