Reply to Comment by Brown and Carrington on "Phase-Space Approach to Solving the Time-Independent Schr\"{o}dinger Equation"

Abstract

The Comment of Brown and Carrington Jr. (BC) has two main points: 1) that the contraction idea of Shimshovitz and Tannor (ST) can be used for any DVR basis, not necessarily periodic, and 2) that the biorthogonal basis introduced by ST is unnecessary. We fully agree with the first point and in fact have several works that were in press at the time of the Comment that illustrate this. On the second point we show that BC implicitly use the biorthogonal basis of ST.