4: Potenciales unidimensionales

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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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