from sympy.physics.quantum import Commutator, Dagger, Operator
from sympy import simplify, exp, series
init_printing()
t = Symbol("t")

L1= Operator("L1")
L2= Operator("L2")
L = L1+L2;

Commutator(L1,L2)==0

def expseries(L,t,k):
    return series(exp(L*t),x=t,n=k);
           

expseries(L1+2*L2,t,3)





expseries(L1+L2,t,3)-expseries(L1,t,3)*expseries(L2,t,3)


simplify(expseries(L1+L2,t,3)-expseries(L1,t,3)*expseries(L2,t,3))

expand(simplify(expseries(L1+L2,t,3)-expseries(L1,t,3)*expseries(L2,t,3))).coeff(t,2)


simplify(expseries(L1+L2,t,3)-expseries(L1/2,t,3)*expseries(L2,t,3)*expseries(L1,t,3))

simplify(expseries(L1+L2,t,4)-expseries(L1/2,t,4)*expseries(L2,t,4)*expseries(L1/2,t,4))

expand(Out[222]).coeff(t,3)