%0 Journal Article
%T Part¨ªcula confinada en una cavidad esferoidal prolata: Algunos efectos de la p¨¦rdida de simetr¨ªa esf¨¦rica
%A A. Castellanos Moreno
%A A. Castellanos Jaramillo
%J Revista mexicana de f¨ªsica E
%D 2012
%I Sociedad Mexicana de F¨ªsica
%X Se estudia el problema de una part¨ªcula confinada en una caja esferoidal prolata. Usando software Mathematica se grafican las funciones esferoidales que aparecen en seis estados f¨ªsicos. Se calculan los niveles de energ¨ªas que se encuentran por debajo de 8.5 rydbergs cuando el inverso de la excentricidad es ¦Î0 = 3 y ¦Î0 = 30. Se compara con el espectro de energ¨ªa de part¨ªcula confinada en una esfera del mismo volumen y se encuentra que cada nivel de este sistema se desdobla en l + 1 niveles cuando se pasa de simetr¨ªa esf¨¦rica a simetr¨ªa prolata. Se estudian los elementos de matriz para interacci¨®n dipolar y se obtiene que la luz emitida o absorbida esta circularmente polarizada. Se calcula el momento dipolar el¨¦ctrico del estado base y de tres estados excitados. Se calculan los coeficientes Aij de Einstein para seis transiciones permitidas. La sencillez del trabajo de computo nos permite sugerir que este material es did¨¢cticamente ¨²til para comprender qu¨¦ sucede en un sistema cu¨¢ntico cuando se modifica su simetr¨ªa. Se sugieren actividades que podr¨ªa realizar un estudiante de licenciatura. The problem being studied is that of a particle moving unimpeded that is confined within a spheroidal box. Using the software Mathematica the spheroidal functions are plotted for six physical states. The energy levels below 8.5 rydbergs are calculated when the inverse of the excentricity ¡êo is taken to be ¦Î0 = 3 and ¦Î0 = 30. A comparison is drawn between the energy spectrum of a particle confined within a spherical box of the same volume, and it is found that every level of this system is split in l + 1 levels when its spherical symmetry is shifted to a prolate symmetry. The matrix elements for dipolar interaction are studied and it is shown that the light that is either emitted or absorbed is circularly polarized. The electric dipole moment is calculated for the ground state and for three further excited states. Einstein's Aij coefficients are calculated for six allowed transitions. The simplicity of the computer work being done allows us to suggest that this material is didactically useful to understand key aspects of what happens within a quantum system in the event that its symmetry is modified. Activities are suggested that could be performed by undergraduate students.
%K M¨¦todos de ense anza
%K t¨¦cnicas computacionales
%K puntos cu¨¢nticos
%K funciones esferoidales
%K Teaching methods
%K computational techniques
%K quantum dots
%K spheroidal functions
%U http://www.scielo.org.mx/scielo.php?script=sci_arttext&pid=S1870-35422012000100004