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4: Potenciales unidimensionales

Última actualización

30 oct 2022
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- 3.11: Ejercicios
- 4.1: Pozo Potencial Infinito

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En este capítulo, investigaremos la interacción de una partícula no relativista de masa $m$ y energía $E$ con diversos potenciales unidimensionales, $V(x)$ . Debido a que estamos buscando soluciones estacionarias con energías únicas, podemos escribir la función de onda en la forma (ver Sección [sstat])

$\psi(x,t) = \psi(x)\,{\rm e}^{-{\rm i}\,E\,t/\hbar},$ donde

$\psi(x)$ satisface la ecuación de Schrödinger independiente del tiempo:

$\label{e5.2} \frac{d^{\,2} \psi}{d x^{\,2}} = \frac{2\,m}{\hbar^{\,2}} \left[V(x)-E\right]\psi.$ En general, la solución,

$\psi(x)$ , a la ecuación anterior debe ser finito, de lo contrario la densidad de probabilidad se

$|\psi|^{\,2}$ volvería infinita (lo cual no es físico). Asimismo, la solución debe ser continua, de lo contrario la corriente de probabilidad ([eprobc]) se volvería infinita (que también es poco física).

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