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On the Schrödinger’s equation
Domènech Masana, Romà
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; González Nogueras, María del Mar
In this article we derive the solution to the Schrödinger's equation in one dimension for a simple example, also the solution to the eigenvalue problem in a three dimensional ball, and then apply the results to deduce the eigenvalues of the Schrödinger's equation for the Hydrogen atom. This eigenvalues give rise to the energy emission lines of the Hydrogen. We also solve the initial-value problem of the Schrödigner's equation in $\R^n$ and the Nonlinear Schrödinger's equation locally, in $\R^3$. We explain the theoretical principles that underly the electronic orbitals of the atom, and deduce their approximated three dimensional aspect.\\
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
Differential equations, Partial
Schrodinger
Partial differential equations
Spherical harmonics
Quantum mechanics
Hydorgen atom
Nonlinear
Equacions en derivades parcials
Classificació AMS::35 Partial differential equations::35Q Equations of mathematical physics and other areas of application
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/bachelorThesis
Universitat Politècnica de Catalunya
         

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