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Consider an infinite square well of width $a$ where the potential $V(x)$ is zero for $0\leq x\leq a$ and infinite otherwise (i.e. for $x>a$ and $x<0$). \subsection*{a)} State de boundary conditions on $\psi(x)$ \subsection*{b)} write down the general solution for $\psi(x)$ (in terms of 2 arbitrary constants) for $E=0$ and for $E<0$. Impose the boundary conditions and show that for each case this lead to a solution that is not valid. \subsection*{c)} write down the general solution for $\psi(x)$ (in terms of 2 arbitrary constants) for $E>0$ expressed in terms of $k=\sqrt{2m E/\hbar^2}$ . By imposing the boundary conditions, solve for $k$ and the Energy level $E_n$ . find the stationary state and Normalized them. \subsection*{d)} Explain briefly why the lower energy level is not zero