1

The following code generates:

enter image description here

You can see that the first and the second line are centered on the right side of the left brace.

How can I stick to the current code implementing "\begin{matrix}" and achieve:

  1. aligning "a(E)" in both lines to the left

  2. aligning "if" to the left

so that two "a"s and "i"s can be aligned together.

enter image description here

\text{when} \left\{\begin{matrix}
a(E)'=\infty, &\text{if }E=\bar{L} \\ 
a(E)'=0, &\text{if }E=0  
\end{matrix}\right.
2

You're using the wrong tool: matrix centers each cell.

\begin{equation*}
\text{when }
\begin{cases}
a(E)'=\infty, &\text{if $E=\bar{L}$} \\ 
a(E)'=0, &\text{if $E=0$}
\end{cases}
\end{equation*}

demo

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