2024-03-19T10:53:27Zhttps://repositori.uji.es/oai/requestoai:repositori.uji.es:10234/1643562019-11-18T18:29:41Zcom_10234_71324com_10234_158176col_10234_98504
Repositori UJI
author
Ortega Moreno, Belen
other
Universitat Jaume I. Departament de Química Física i Analítica
2016-11-10T12:36:49Z
2016-11-10T12:36:49Z
2016-09-22
http://hdl.handle.net/10234/164356
In this project we will apply the variational method to the problem of particle enclosed in a onedimensional
box. Quantum mechanical calculations of complex many-body systems often employ
approximate methods because of the difficulty in solving the Schröedinger equation exactly.
Undergraduate textbooks of physical chemistry normally treat these approximate methods
qualitatively because they require a mathematical sophistication beyond that of the students. This
makes difficult for the student to appreciate the difference between eigenfunctions (exact wave
functions) derived from exact solutions of the Schröedinger equation and approximate wave
functions generated by using approximate quantum mechanical techniques.
It is suggested in this ok that a rigorous set of calculations can be done using a trial approximate
wave function on a simple quantum mechanical system for which the exact solution is known.
The simplest quantum mechanical system for which a particle is in a bound state is the so-called
“particle in a box” were a particle is constrained in a region of constant potential energy in the
interval, 0 < x < a. At x = 0 and x = a, the potential energy rises discontinuously to infinity. What
follows is a description of this system employing an approximate wave function.
This project seems to me an excellent proposal for the quantum chemistry practices for
undergraduate students, as it is a method studied in but usually because it needs to be solved by
heavy computational methods, it does not fit to standard sessions of problems.
eng
Grau en Química
Grado en Química
Bachelor's Degree in Chemistry
Partículas (Materia)
Química cuántica
Mecánica cuántica
Métodos computacionales
Funciones de onda
Application of the Variational Method to the particle in the box problem : the problem of the choice of base set
info:eu-repo/semantics/bachelorThesis
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
URL
https://repositori.uji.es/xmlui/bitstream/10234/164356/1/TFG_Ortega_Moreno%2C_Belen.pdf
File
MD5
fc978b99fc7df171579a354eebbd8c9a
4164538
application/pdf
TFG_Ortega_Moreno,_Belen.pdf
URL
https://repositori.uji.es/xmlui/bitstream/10234/164356/5/TFG_Ortega_Moreno%2C_Belen.pdf.txt
File
MD5
070d3eb6ea16972f9384e444a16e2d89
17349
text/plain
TFG_Ortega_Moreno,_Belen.pdf.txt