The bound states of Dirac equation with a scalar potential

Dwivedi, Vatsal

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https://hdl.handle.net/2142/89002 Copy

Description

Title

The bound states of Dirac equation with a scalar potential

Author(s)

Dwivedi, Vatsal

Issue Date

2015-12-10

Director of Research (if dissertation) or Advisor (if thesis)

Bronski, Jared

Department of Study

Mathematics

Discipline

Applied Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

• Dirac equation
• Bound states
• Dynamical systems

Abstract

"We study the bound states of the 1+1 dimensional Dirac equation with a scalar potential, which can also be interpreted as a position dependent ""mass'', analytically as well as numerically. We derive a Prüfer-like representation for the Dirac equation, which can be used to derive a condition for the existence of bound states in terms of the fixed point of the nonlinear Prüfer equation for the angle variable. Another condition was derived by interpreting the Dirac equation as a Hamiltonian flow on the 2-dimensional Euclidean space and a shooting argument for the induced flow on the space of its Lagrangian planes following a similar calculation by Jones (Ergodic Theor Dyn Syst, 8 (1988) 119-138). The two conditions are shown to be equivalent, and used to compute the bound states analytically and numerically, as well as to derive a Calogero-like upper bound on the number of bound states. The analytic computations are also compared to the bound states computed using techniques from supersymmetric quantum mechanics."

Graduation Semester

2015-12

Type of Resource

text

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http://hdl.handle.net/2142/89002

Copyright and License Information

Copyright 2015 Vatsal Dwivedi

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