How is the Schrödinguer equation actually solved? Three different methods to address the Quantum Harmonic Oscillator problem
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How is the Schrödinguer equation actually solved? Three different methods to address the Quantum Harmonic Oscillator problemAuthor (s)
Tutor/Supervisor; University.Department
Climente, Juan I.; Sancho Llopis, Juan Vicente; Universitat Jaume I. Departament de Química Física i AnalíticaDate
2020-06-26Publisher
Universitat Jaume IAbstract
Quantum chemistry is a central subject in Chemistry degree because it provides ultimate answers to
explain reactivity, structural, stability and spectroscopy of atoms molecules and solids. However, to
derive practical ... [+]
Quantum chemistry is a central subject in Chemistry degree because it provides ultimate answers to
explain reactivity, structural, stability and spectroscopy of atoms molecules and solids. However, to
derive practical conclusions, one need to be familiar with several specific mathematical concepts
and techniques. Undergraduate courses on Quantum Chemistry often omit much of this
mathematical background in order to highlight the physical concepts, as doing otherwise would
likely confuse the majority of students. Who would “not see the forest because of the leaves”. As a
result, the solutions of the Schrödinguer equation are usually provided right after presenting the
Hamiltonian. Obviously, a student with interest in the matter realizes he is missing an important
step, for he is then unable to obtain solutions autonomously.
The goal of this work is to provide an introductory view on some of the mathematical tools used in
Quantum Chemistry to obtain eigenvalues and eigenstates of the time-independent Schrödinguer
equation. Namely, we study polynomial method, the factorization method and the method of finite
differences. All three techniques are applied to solve the Quantum Harmonic oscillator problem. We
purpose fully fully choose this problem because it is pervasive in most areas of Physical Chemistry,
and susceptible of being solved through any of the techniques, which will allow us to draw
comparisons and conclusions in the end. [-]
Subject
Description
Treball Final de Grau en Química. Codi: QU0943. Curs acadèmic: 2019/2020
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info:eu-repo/semantics/bachelorThesisRights
info:eu-repo/semantics/openAccess
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- Grau en Química [265]