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\centerline{\textbf{Particle in an Infinite Square Well Potential 1}}
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A particle of mass $m$ is in an infinite square well potential at $0<x<L$. 

The particle is initially in the state:

$$|\psi(t=0)\rangle = A \left( |\varphi_1)\rangle + 2i |\varphi_4\rangle - 3|\varphi_{10}\rangle \right)$$

\begin{enumerate}
\item	Determine $A$
\item	At $t=0$ what is the probability of measuring the energy of the particle to be $\frac{8\pi^2\hbar^2}{mL^2}$?
\item Find state of the particle at a later time $t$.
\item	What is the probability of measuring the energy of the particle to be the same value at a later time $t$?
\end{enumerate}




\vfill
\leftline{\textit{by Elizabeth Gire}}
\leftline{\copyright 2/7/2017 Elizabeth Gire}
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