A linear variational exercise with a simple non-orthogonal basis for the particle-in-the-box problem

作者：Luana Victor^*; Otero de la Roza A; Blanco M A; Recio J M

来源：European Journal of Physics, 2010, 31(1): 101-114.

DOI：10.1088/0143-0807/31/1/010

The particle-in-the-box, with or without an additional potential, is proposed as an excellent laboratory to teach and explore the details of the linear variational method using a non-orthogonal basis. The x(n)(a-x)(n) and x(n)(a/2-x)(a-x)(n) polynomials are shown to form a complete basis for the even and odd states, respectively, of the particle confined to the x. [0, a] interval. A short and simple Octave code is presented as the natural extension to the hand calculations when the basis set grows in size.

• 出版日期2010-1