Consider a particle in one dimensional square well potential \begin{equation} V(x) = \left\{ \begin{array}{ll} 0 & 0 \le x \le L \\ V_0 & \mbox{otherwise} \end{array} \right. \end{equation} For a bound state we should have average energy less than V_0$. $$ \langle E\rangle =\langle T\rangle + \langle V\rangle < V_0 $$ where $\langle T\rangle$ and $\langle V\rangle$ are the averages of the kinetic and the potential energies, respectively. If the article is to be confined to a region of size $L$, use the uncertainty principle to get a rough estimate of average kinetic energy, $\langle T\rangle$. Use this to find approximate minimum value of $V_0a^2$ required for a bound state to exist. |
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4727:Diamond Point
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