  Superconductivity is usually described in the framework of the
Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the
resonating-valence-bond (RVB) wavefunction proposed for the high-temperature
superconductivity in the cuprate. A natural question is \emph{if} any
fundamental physics could be possibly missed by applying such a scheme to
strongly correlated systems. Here we study the pairing wavefunction of two
holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using
variational Monte Carlo (VMC) approach. By comparing with density matrix
renormalization group (DMRG) calculation, we show that a conventional BCS or
RVB pairing of the doped holes makes qualitatively wrong predictions and is
incompatible with the fundamental pairing force in the $t$-$J$ model, which is
kinetic-energy-driven by nature. By contrast, a non-BCS-like wavefunction
incorporating such novel effect will result in a substantially enhanced pairing
strength and improved ground state energy as compared to the DMRG results. We
argue that the non-BCS form of such a new ground state wavefunction is
essential to describe a doped Mott antiferromagnet at finite doping.
