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Quantum mechanical three-body problem with short-range interactions

Mohr, Richard Frank, Jr.
http://rave.ohiolink.edu/etdc/view?acc_num=osu1050007430

Abstract Details

2003, Doctor of Philosophy, Ohio State University, Physics.
We have investigated S-wave bound states composed of three identical bosons interacting via regulated delta function potentials in non-relativistic quantum mechanics. For low-energy systems, these short-range potentials serve as an approximation to the underlying physics, leading to an effective field theory. A method for perturbatively expanding the three-body bound-state equation in inverse powers of the cutoff is developed. This allows us to extract some analytical results concerning the behavior of the system. Further results are obtained by solving the leading order equations numerically to 11 or 12 digits of accuracy. The limit-cycle behavior of the required three-body contact interaction is computed, and the cutoff-independence of bound-state energies is shown. By studying the relationship between the two- and three-body binding energies, we obtain a high accuracy numerical calculation of Efimov's universal function. Equations for the first order corrections, necessary for the study of cutoff dependence, are derived. However, a numerical solution of these equations is not attempted.
Robert Perry (Advisor)
182 p.
Physics, Nuclear
quantum mechanics; three-body problem; delta function potential; Efimov function; uniform expansion

Recommended Citations

Citations

  • Mohr, Jr., R. F. (2003). Quantum mechanical three-body problem with short-range interactions [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1050007430

    APA Style (7th edition)

  • Mohr, Jr., Richard. Quantum mechanical three-body problem with short-range interactions. 2003. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1050007430.

    MLA Style (8th edition)

  • Mohr, Jr., Richard. "Quantum mechanical three-body problem with short-range interactions." Doctoral dissertation, Ohio State University, 2003. http://rave.ohiolink.edu/etdc/view?acc_num=osu1050007430

    Chicago Manual of Style (17th edition)

osu1050007430
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© 2003, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.