# How is this a condition for a Majorana zero mode?

EDIT: Nevermind, I figured it out. When you apply the expression on a state, you can clearly see what it does: The new state created by applying the Majorana operators must have the same energy as the original one. So when applied on a zero-energy state, this creates a degeneracy and the so-called Majorana zero mode.

I am currently trying to grasp this lecture by Frank Wilczek about Majorana zero modes on an 1-dimensional wire. In equation (31), he states that a general condition for such a zero mode is $$\left[ H, \sum_{j=1}^{2L} c_j \gamma_j \right] = 0,$$ where the $c_j$ are coefficients and the $\gamma_j$ are the Majorana operators for the sites of the chain. I'm not sure I understand why this is a general condition for a zero mode if the two operators commute. Can anyone shed some light on this?