How to get the solution of idU(t)/dt=H(t)U(t)

[mathemaphysis]

i have a problem, please help me,
i need to implement a numerical method to solve the following Schrödinger equation:
idU(t)/dt=H(t)U(t)
with:
U(0)=1 (identity matrix)
U(T)=U_T (U_T is some given unitary operator)
where : H(t) is the Hamiltonian of the system, and
U(t) is a unitary operator
dimension of the operators is N*N (N is a non zero integer)

 

[mathemaphysis]

the above problem is an ordinary diffirential equation, i know how to deal with ODE when the unknown is a real function, but when the unknown is an operator, i am confused.

thank you

 

[mathemaphysis]

i just need basic steps, i don't need all the details

thank you