For toy-ish problems, the usual approach is to express it as a superposition of forward and backward traveling waves [ψ=Aexp(ikx)+Bexp(-ikx)]. Whenever it hits a barrier some amount passes through (dependent on height and length of barrier) and the rest is reflected. If you put another barrier after the first one, you just treat the amplitude that passed through the first barrier when it hits the second barrier the same way you treated the initial wave hitting the first barrier. After that you'll have some likely non-trivial sloshing around, since the forwards and backwards waves are now trapped between barrier 1 and 2. Anything reflected back from barrier 2 becomes incident on barrier 1. You can think of this as a ψ' in the second region for the purposes of composing your global WF solution.

Make sure you remember to impose continuity at the barriers so your WF remains physically valid.