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Supersymmetry in Quantum Mechanics

Kuberski, Simon LU (2014) FYTK01 20141
Theoretical Particle Physics - Has been reorganised
Department of Astronomy and Theoretical Physics - Has been reorganised
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... (More)
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. (Less)
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author
Kuberski, Simon LU
supervisor
organization
course
FYTK01 20141
year
type
M2 - Bachelor Degree
subject
keywords
supersymmetric quantum mechanics, partner potentials, quantum mechanics, partner Hamiltonian, shape invariant potential, shape invariance, Morse potential
language
English
id
4457982
date added to LUP
2014-06-17 07:56:07
date last changed
2017-10-06 16:57:18
@misc{4457982,
  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.}},
  author       = {{Kuberski, Simon}},
  language     = {{eng}},
  note         = {{Student Paper}},
  title        = {{Supersymmetry in Quantum Mechanics}},
  year         = {{2014}},
}