Essays about: "eigenfunctions"

Showing result 1 - 5 of 9 essays containing the word eigenfunctions.

1. 1. Oscillations in a complex sunspot: From theory to data

   University essay from Luleå tekniska universitet/Institutionen för system- och rymdteknik

   Author : Femke Kranenbarg; [2024]
   Keywords : ;

   Abstract : Sunspot oscillations, intricate three-dimensional wave-like motions in the solar atmosphere, result from the complex interplay between plasma and magnetic fields. This study delves into the behaviour of these oscillations, exploring their simultaneous excitation and evaluating their impact on solar phenomena like coronal heating, energy transport, and solar flares. READ MORE

3. 2. Exact eigenstates of the Inozemtsev spin chain

   University essay from KTH/Fysik

   Author : Simon Lentz; [2021]
   Keywords : Theoretical physics; Mathematical physics; quantum mechanics; many-body problems; spin chain; Inozemtsev; Calogero-Sutherland; Teoretisk fysik; Matematisk fysik; kvantmekanik; mångpartikel problem; spinnkedjor; Inozemtsev; Calogero-Sutherland;

   Abstract : This thesis deals with the following question: are there more eigenfunctions, other than the already known eigenfunctions, of the spin chain with elliptic interactions known as the Inozemtsev spin chain? The Inozemtsev spin chain interpolates between two quantum integrable spin chains, theHeisenberg spin chain and the Haldane-Shastry spin chain. Therefore it is interesting to explore eigenfunctions of the Inozemtsev spin chain in greater detail. READ MORE

4. 3. 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

5. 4. Feigenbaum Scaling

   University essay from Linnéuniversitetet/Institutionen för matematik (MA)

   Author : Janek Sendrowski; [2020]
   Keywords : Feigenbaum; Feigenbaum constant; Feigenbaum point; superstable; self-similarity; fractals; final-state diagram; logistic map; period-doubling operator; linearized period-doubling operator; Cantor set; Sharkovsky sequence; Chebyshev interpolation; stable manifold; unstable manifold; orbits; fixed points; scaling factor; pitchfork bifurcation; cobweb plot; renormalization; iterates; one-hump map; unimodal map; bifurcation cascade; Feigenbaum universality; chaos theory; spectrum; generalized Feigenvalues; bifurcation points; superstable points; fixed function; universal function; eigenvalues; eigenvectors; eigenfunctions; universality conditions; Schwarzian derivative; Newton’s method; power method; Arnoldi’s method; attractive fixed point; repellent fixed point; Banach fixed-point theorem; collocation method; functional analysis; topology;

   Abstract : In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. READ MORE

6. 5. IR spectroscopy for vibrational modes : A semi-classical approach based on classical electrodynamicsand modern quantum mechanics

   University essay from Linnéuniversitetet/Institutionen för fysik och elektroteknik (IFE)

   Author : Ulf Oreborn; [2018]
   Keywords : ;

   Abstract : The atoms of a molecule are always restless and are constantly moving in one way or another.Apart from rotations and translations, they may vibrate in many different modes. They may moveradially toward or from each other, so called stretching. This can be done symmetrically or asymmetrically. READ MORE