Two and Three Versus One-Dimensional Problems

Abstract

The one-dimensional Schrödinger equation for a particle in a potential V₁ (x) is

$$ \left\{ { - \frac{{\hbar ^2 }} {{2m}}\frac{{d^2 }} {{dx^2 }} + V_1 (x)} \right\}\psi _n (x) = E_n \psi _n (x), $$

((8.1))

where

$$ \int\limits_{ - \infty }^{ + \infty } {\left| {\psi _n (x)} \right|^2 dx = 1.} $$

.