Slepian eigenvalues as tunnelling rates

We calculate the eigenvalues of an integral operator associated with Prolate Spheroidal Wave Functions (or Slepian functions) by interpreting them as tunnelling probabilities in analogous quantum problem. Doing so allows us to extend a well-known approximation due that it applies outside important transition region where these pass from being near unity zero. Study has traditionally been problems arising signal analysis and optics but have more recently found relevance quantifying channel strengths available Multiple-In Multiple-Out (MIMO) radio communication. The approach presented promises easier generalisation broader range geometries possible latter context.