Application of the Variational Method to the particle in the box problem : the problem of the choice of base set
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Application of the Variational Method to the particle in the box problem : the problem of the choice of base setAutoria
Tutor/Supervisor
Rajadell Viciano, FernandoTutor/Supervisor; Universitat.Departament
Universitat Jaume I. Departament de Química Física i AnalíticaData de publicació
2016-09-22Editor
Universitat Jaume IResum
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 ... [+]
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. [-]
Paraules clau / Matèries
Descripció
Treball Final de Grau en Química. Codi: QU0943. Curs: 2015/2016
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- Grau en Química [265]