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[QUE/QM-07002]

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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.
 squqre qell

 

 

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