using DifferentialEquations
using LinearAlgebra

σx = [0.0+0.0im 1.0; 1.0 0]

function hfun(t)
    σx
end

function f(du, u, p, t)
    hmat = hfun(t)
    mul!(du, -1.0im*hmat, u)
end

function f_jac(J, u, p, t)
    hmat = hfun(t)
    mul!(J, -1.0im, hmat)
end

ff = ODEFunction(f;jac=f_jac)
tspan = (0.0, 10.0)
u0 = [1.0+0.0im, 0]
prob = ODEProblem(ff, u0, tspan)
sol = solve(prob,TRBDF2(),reltol=1e-8,abstol=1e-8)