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Simon Kuberski
Supersymmetry in Quantum Mechanics
Abstract
This thesis gives an introduction to the basic formalism of one-dimensional supersymmetric quantum mechanics. The factorization of a Hamiltonian is used to create a supersymmetric partner Hamiltonian. The connections between the energy spectra and wave functions of these partner Hamiltonians are deduced and examined for the case of broken and unbroken supersymmetry. An extension to hierarchies of Hamiltonians is made and used to describe shape invariant potentials. The formalism is used to solve some textbook examples like the infinite square well and the harmonic oscillator potential in a new way and to determine the wave functions and energy levels of the hydrogen atom in a nonrelativistic and a relativistic treatment. A two-dimensional extension of the formalism is introduced and applied to find a way to solve the eigenvalue problem for a matrix Pauli Hamiltonian through its scalar partner Hamiltonians. The two-dimensional formalism is further used to examine a chain of two- dimensional real singular Morse potentials and to determine the wave functions and energy spectra based on the solution of the one-dimensional Morse potential.
LU TP 14-13
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