I am working on a formulae in a notes. Here is part of my code,

\begin{equation*} \phi(x) := \left\{ \begin{aligned} &\chi_{K_n}(\bar{x})\cdot\frac{\psi_n(x)}{\tilde{\psi}_n(\bar{x})}, & \text{ if } \bar{x}\in K_n \\ &0 & \text{ otherwise} \end{aligned} \right. \end{equation*} 

The problem is that I need a subcript of a subscript in \chi_{K_n}, but \chi is a small letter, K is a capital letter. With a small subscript n on the right, it looks like \chi times K_n, is there a way to make \chi bigger or make the subscript K smaller? Thanks.

By the way, can I post math formulae here like I do in mathstakexchange?