Time-of-Flight Signatures of Bosons in a Double Well

We present analytical and numerical treatments for evaluating the time-of-flight momentum distribution for the stationary states of a two-boson system trapped in a quartic double-well potential, paying particular attention to the Tonks and noninteracting regimes. We find that the time-of-flight distributions can serve as a valuable tool in profiling the states of this system, and provide the tof plots for low-energy excitations using a nonadaptive finite element method that is more efficient than traditional finite difference methods.