- #1
Rob Turrentine
- 9
- 0
So there's a free particle with mass m.
\begin{equation}
\psi(x,0) = e^{ip_ox/\hbar}\cdot\begin{cases}
x^2 & 0 \leq x < 1,\\
-x^2 + 4x -2 & 1 \leq x < 3,\\
x^2 -8x +16 & 3 \leq x \leq 4, \\
0 & \text{otherwise}.
\end{cases}
\end{equation}
What does each part of the piecewise represent? And what are the boundary conditions representative of? Energy levels?
I'm used to working with non-piecewise functions, like \begin{equation} \psi = Ae^{ikx} + Be^{-ikx} \end{equation}
so I'm just not sure what to do.
The goal is to normalize it and then find <X> and <P> as functions of time.
Any help is greatly appreciated!
\begin{equation}
\psi(x,0) = e^{ip_ox/\hbar}\cdot\begin{cases}
x^2 & 0 \leq x < 1,\\
-x^2 + 4x -2 & 1 \leq x < 3,\\
x^2 -8x +16 & 3 \leq x \leq 4, \\
0 & \text{otherwise}.
\end{cases}
\end{equation}
What does each part of the piecewise represent? And what are the boundary conditions representative of? Energy levels?
I'm used to working with non-piecewise functions, like \begin{equation} \psi = Ae^{ikx} + Be^{-ikx} \end{equation}
so I'm just not sure what to do.
The goal is to normalize it and then find <X> and <P> as functions of time.
Any help is greatly appreciated!