Essays about: "Hamiltonian Operator"

Showing result 1 - 5 of 8 essays containing the words Hamiltonian Operator.

1. 1. Asymptotic Symmetries and Dressed States in QED and QCD

   University essay from Stockholms universitet/Fysikum

   Author : Saimeng Zhou; [2023]
   Keywords : Dressed states; Large gauge transformation; Faddeev-Kulish formalism; Generalized coherent state operator; Wilson line; Infrared divergence; Asymptotic Hamiltonian; QED; QCD;

   Abstract : Infrared divergences arising in theories with massless gauge bosons have been shown to cancel in scattering amplitudes when using dressed states constructed from the Faddeev- Kulish approach to the asymptotic states. It has been established that these states are closely related to asymptotic symmetries of the theory, that is, non-vanishing gauge trans- formations at the asymptotic boundary. READ MORE

3. 2. An Introduction to Hitchin Systems

   University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

   Author : Manuel Neumayer; [2023]
   Keywords : Mathematics and Statistics;

   Abstract : This thesis aims to introduce the tools that are needed to understand — and historically led to the inception of — Hitchin systems. We lay out a basic theory of Hamiltonian systems on symplectic manifolds, and prove the Liouville-Arnold theorem, which states that integrable Hamiltonian systems admit coordinates in which their solution is basically linear. READ MORE

4. 3. Dynamics at an exceptional point in an interacting quantum dot system

   University essay from Lunds universitet/Fasta tillståndets fysik; Lunds universitet/Fysiska institutionen

   Author : William Samuelson; [2022]
   Keywords : Physics and Astronomy;

   Abstract : A fundamental postulate of quantum mechanics is that the Hamiltonian of a closed system is Hermitian, guaranteeing real-valued energies and conserved probabilities throughout the evolution of the system. However, for quantum systems where there is dissipation and crosstalk with the environment, such as a system of quantum dots connected to an environment of metallic leads, the dynamics of the system is instead generated by a non-Hermitian Liouvillian superoperator. READ MORE

5. 4. A Mathematical Analysis of the Harmonic Oscillator in Quantum Mechanics

   University essay from Linnéuniversitetet/Institutionen för matematik (MA)

   Author : Philip Solarz; [2021]
   Keywords : Functional Analysis; Quantum Mechanics; Harmonic Oscillator; Schrödinger Equation; Hamiltonian Operator; Hermite Functions; Hilbert Space; Schatten-von Neumann Operator; Mehler s Formula;

   Abstract : In this paper we derive the eigenfunctions to the Hamiltonian operator associated with the Harmonic Oscillator, and show that they are given by the Hermite functions. Then we prove that the Hermite functions form an orthonormal basis in the underlying Hilbert space. READ MORE

6. 5. Finite-dimensional PT-symmetric Hamiltonians with an application to neutrino oscillations

   University essay from KTH/Skolan för teknikvetenskap (SCI)

   Author : Alexander Fagerlund; Chistopher Ekman; [2020]
   Keywords : ;

   Abstract : In this report, we first briefly summarize Hermitian quantum mechanics before moving on to the non-Hermitian case. We then review PT-symmetric quantum mechanics with a focus on finite-dimensional systems, and include a novel generalization of a perturbative calculation of the C-operator. READ MORE