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Relevant bibliographies by topics / Time-dependent Schrödinger equation

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Academic literature on the topic 'Time-dependent Schrödinger equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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Dissertations / Theses on the topic "Time-dependent Schrödinger equation"

1

Nissen, Anna. "Absorbing boundary techniques for the time-dependent Schrödinger equation." Licentiate thesis, Uppsala universitet, Avdelningen för teknisk databehandling, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-113087.

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Chemical dissociation processes are important in quantum dynamics. Such processes can be investigated theoretically and numerically through the time-dependent Schrödinger equation, which gives a quantum mechanical description of molecular dynamics. This thesis discusses the numerical simulation of chemical reactions involving dissociation. In particular, an accurate boundary treatment in terms of artificial, absorbing boundaries of the computational domain is considered. The approach taken here is based on the perfectly matched layer technique in a finite difference framework. The errors intro

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2

Viklund, Lina, Louise Augustsson, and Jonas Melander. "Numerical approaches to solving the time-dependent Schrödinger equation with different potentials." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-295932.

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This project is an immersive study in numerical methods, focusing on quantum molecular dynamics and methods for solving the time-dependent Schrödinger equation. First the Schrödinger equation was solved with finite differences and a basic propagator in time, and it was then concluded that this method is far too slow and compuationally heavy for its use to be justified for this type of problem. Instead pseudo-spectral methods with split-operators were implemented, and this proved to be a far more favourable method for solving, both in regards to time and memory requirements. Further, the pseudo

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3

Fathe, Jalali Atabak, and Hugo Åkesson. "Comparing Three Numerical Methods For Solving The 1D Time Dependent Schrödinger Equation." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297532.

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The purpose of this thesis is to implement three numerical methods for solving and examining the time-dependent Schrödinger equation (TDSE) of the analytically solved quantum harmonic oscillator (QHO) and the, to our knowledge, analytically unsolved double well potential (DW), and to compare the numerical solutions. These methods are the Crank-Nicolson method and two split operator methods of different orders. For the QHO, the exact solution is used to determine the errors of the methods, while other methods for examining the DW had to be used (due to the lack of exact solutions). The solution

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4

Johansson, Karoline. "A counterexample concerning nontangential convergence for the solution to the time-dependent Schrödinger equation." Thesis, Växjö University, School of Mathematics and Systems Engineering, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1082.

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<p>Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+ $ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|

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5

Capel, Pierre. "Coulomb breakup of halo nuclei by a time-dependent method." Doctoral thesis, Universite Libre de Bruxelles, 2004. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211186.

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Halo nuclei are among the strangest nuclear structures.<p>They are viewed as a core containing most of the nucleons<p>surrounded by one or two loosely bound nucleons. <p>These have a high probability of presence at a large distance<p>from the core.<p>Therefore, they constitute a sort of halo surrounding the other nucleons.<p>The core, remaining almost unperturbed by the presence<p>of the halo is seen as a usual nucleus.<p><p><P><p><p>The Coulomb breakup reaction is one of the most useful<p>tools to study these nuclei. It corresponds to the<p>dissociation of the halo from the core during a coll

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6

Kopylov, Nikita. "Magnus-based geometric integrators for dynamical systems with time-dependent potentials." Doctoral thesis, Universitat Politècnica de València, 2019. http://hdl.handle.net/10251/118798.

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[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los o

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7

Grandin, Magnus. "Adaptive Solvers for High-Dimensional PDE Problems on Clusters of Multicore Processors." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-234984.

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Accurate numerical solution of time-dependent, high-dimensional partial differential equations (PDEs) usually requires efficient numerical techniques and massive-scale parallel computing. In this thesis, we implement and evaluate discretization schemes suited for PDEs of higher dimensionality, focusing on high order of accuracy and low computational cost. Spatial discretization is particularly challenging in higher dimensions. The memory requirements for uniform grids quickly grow out of reach even on large-scale parallel computers. We utilize high-order discretization schemes and implement ad

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8

Kieri, Emil. "Numerical Methods for Wave Propagation : Analysis and Applications in Quantum Dynamics." Doctoral thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-268625.

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We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. In most settings, numerical solution of the TDSE is more challenging than solving a hyperbolic wave equation. This is mainly because the dispersion relation of the TDSE makes it very sensitive to dispersion error, and infers a stringent time step restriction for standard explicit time stepping schemes. The TD

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9

Hashemloo, Avazeh. "Numerical simulation of the dynamics of a trapped molecular ion." Doctoral thesis, Umeå universitet, Institutionen för fysik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-118899.

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This thesis explores the dynamics of a heteronuclear diatomic molecular ion, possessing a permanent electric dipole moment, µ, which is trapped in a linear Paul trap and can interact with an off-resonance laser field. To build our model we use the rigid-rotor approximation, where the dynamics of the molecular ion are limited to its translational and rotational motions of the center-of-mass. These dynamics are investigated by carrying out suitable numerical calculations. To introduce our numerical methods, we divide our research topic into two different subjects. First, we ignore the rotational

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10

Johansson, Karoline. "Propagation of singularities for pseudo-differential operators and generalized Schrödinger propagators." Licentiate thesis, Linnaeus University, School of Computer Science, Physics and Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-2447.

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<p>In this thesis we discuss different types of regularity for distributions which appear in the theory of pseudo-differential operators and partial differential equations. Partial differential equations often appear in science and technology. For example the Schrödinger equation can be used to describe the change in time of quantum states of physical systems. Pseudo-differential operators can be used to solve partial differential equations. They are also appropriate to use when modeling different types of problems within physics and engineering. For example, there is a natural connection bet

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