This undergraduate thesis contains one dimensional introductory treatment of Supersymmetric Quantum Mechanics (SUSY QM). The factorisation method is used to obtain Partner Hamiltonians, and the notions of partner potentials and superpotential are introduced. It demonstrated how energy spectra and eigenfunctions of partner potentials can be correlated for the cases of unbroken and broken supersymmetry. Generalisations of these cases attributed to Sets of Hamiltonians and shape invariant potentials are introduced. The devel oped formalisation is used to obtain energy eigenfunctions and spectra of partner potentials of some well-known quantum systems, namely the Infinite Square Well and the Free Particle. In these systems, the partner potentials are trigonometric and hyperbolic functions, respectively. A comparison of these two physically distinct but mathematically related partner potentials is provided. A new philosophical interpretation of SUSY QM is introduced, with an ontological discussion of supersymmetric notions and SUSY QM. The current observation problem of SUSY is discussed, and on that basis, two opposing arguments are presented. The method of Falsification by Karl Popper is briefly introduced, and an argument is produced regarding its application to SUSY.This undergraduate thesis contains one dimensional introductory treatment of Supersymmetric Quantum Mechanics (SUSY QM). The factorisation method is used to obtain Partner Hamiltonians, and the notions of partner potentials and superpotential are introduced. It demonstrated how energy spectra and eigenfunctions of partner potentials can be correlated for the cases of unbroken and broken supersymmetry. Generalisations of these cases attributed to Sets of Hamiltonians and shape invariant potentials are introduced. The devel oped formalisation is used to obtain energy eigenfunctions and spectra of partner potentials of some well-known quantum systems, namely the Infinite Square Well and the Free Particle. In these systems, the partner potentials are trigonometric and hyperbolic functions, respectively. A comparison of these two physically distinct but mathematically related partner potentials is provided. A new philosophical interpretation of SUSY QM is introduced, with an ontological discussion of supersymmetric notions and SUSY QM. The current observation problem of SUSY is discussed, and on that basis, two opposing arguments are presented. The method of Falsification by Karl Popper is briefly introduced, and an argument is produced regarding its application to SUSY.

Apr 26, 20240 citations

The Quantum Mechanics of Trapped Wave Packets

Roy J. Glauber

Foundations of Quantum MechanicsApr 1, 19925 citations

Supersymmetric Pauli Hamiltonians

Georg Junker

Institute of Physics eBooksJan 1, 20190 citations

Single ion thermal wave packet analyzed via time-of-flight detection

Felix Stopp, Luis Ortiz-Gutiérrez, Henri Lehec +1 more

Abstract A single 40Ca ion is confined in the harmonic potential of a Paul trap and cooled to a temperature of a few mK, with a wave packet of sub-μm spatial and sub-m s−1 velocity uncertainty. Deterministically extracted from the Paul trap, the single ion is propagating over a distance of 0.27 m and detected. By engineering the ion extraction process on the initial wave packet, theoretically modeling the ion trajectories, and studying experimentally the time-of-flight distribution, we directly infer the state of the previously trapped ion. This analysis allows for accurate remote sensing of the previous motional excitation in the trap potential, both coherently or incoherently. Our method paves a way to extract, manipulate and design quantum wave packets also outside of the Paul trap.Abstract A single 40Ca ion is confined in the harmonic potential of a Paul trap and cooled to a temperature of a few mK, with a wave packet of sub-μm spatial and sub-m s−1 velocity uncertainty. Deterministically extracted from the Paul trap, the single ion is propagating over a distance of 0.27 m and detected. By engineering the ion extraction process on the initial wave packet, theoretically modeling the ion trajectories, and studying experimentally the time-of-flight distribution, we directly infer the state of the previously trapped ion. This analysis allows for accurate remote sensing of the previous motional excitation in the trap potential, both coherently or incoherently. Our method paves a way to extract, manipulate and design quantum wave packets also outside of the Paul trap.

arXiv:2102.12947New Journal of PhysicsMay 11, 20216 citations

Expected values for SUSY hierarchies of Jaynes-Cummings Hamiltonian

İsmail Burak Ateş, Şengül Kuru, Javier Negro +1 more

The aim of this letter is to compute the evolution of some expected values, such as the field operators $a^\pm$ , quadratures and atomic inversion, under supersymmetric (SUSY) partner Hamiltonians associated to the Jaynes-Cummings Hamiltonian of quantum optics. This kind of SUSY partners are characterized by having spectra which differ in a finite number of energy levels. We wish to elucidate if the partner connection has any influence on these expected values. In particular, we want also to know in which way the classical and revival times are affected by such SUSY partners.The aim of this letter is to compute the evolution of some expected values, such as the field operators $a^\pm$, quadratures and atomic inversion, under supersymmetric (SUSY) partner Hamiltonians associated to the Jaynes-Cummings Hamiltonian of quantum optics. This kind of SUSY partners are characterized by having spectra which differ in a finite number of energy levels. We wish to elucidate if the partner connection has any influence on these expected values. In particular, we want also to know in which way the classical and revival times are affected by such SUSY partners.

quant-pharXiv:2512.12647Physica ScriptaDec 16, 20250 citations

The aim of this letter is to compute the evolution of some expected values, such as the field operators

a^\pm

, quadratures and atomic inversion, under supersymmetric (SUSY) partner Hamiltonians associated to the Jaynes-Cummings Hamiltonian of quantum optics. This kind of SUSY partners are characterized by having spectra which differ in a finite number of energy levels. We wish to elucidate if the partner connection has any influence on these expected values. In particular, we want also to know in which way the classical and revival times are affected by such SUSY partners.