Abstract

CASTANETA, HERIBERTO  and  NOGALES, JORGE. Solución analítica de la ecuación de Schrodinger independiente del tiempo para una partícula en una caja cuántica. Rev.Cs.Farm. y Bioq [online]. 2015, vol.3, n.1, pp.87-99. ISSN 2310-0265.

In this article, the Schrodinger equa-tion is analyzed and resolved independent of time or steady state, for a particle into a one-dimensional box of zero potential. For this purpose the quantum postulates and concepts are defined like the function of wave and the mathematical requirements to be met such as being continuous function, single-valued (just one value f(x) for each value of x) and differentiable (derivable). The quantum operators are described: such as the operator position, derived operator, operator of classical and quantum momen-tum, potential energy operator, Hamiltonian operator. Own values or eigenvalues are ob-tained. Functions are normalized applying methods of integral calculus and the Schrodinger equation is establish for a dimension and three dimensions. The solution gives to a function of real wave that mathematically it is a sine trigonometric function. It is found that the energy of the particle is quantized or limited to discrete values.

Keywords : Quantum mechanics; Schrodinger equation; one-dimensional box.

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