  Starting from N=2 supersymmetric theories in 2 dimensions, we formulate a
novel time-dependent supersymmetric quantum theory where the R-charge is
twisted along the time. The invariance of the supersymmetric index under
variations of the action for these theories leads to two predictions: In the IR
limit it predicts how the degeneracy of BPS states change as we cross the walls
of marginal stability. On the other hand, its equivalence with the UV limit
relates this to the spectrum of the U(1) R-charges of the Ramond ground states
at the conformal point. This leads to a conceptually simple derivation of
results previously derived using tt* geometry, now based on time-dependent
supersymmetric quantum mechanics.
