Two operators A and B satisfy the commutation relations [H, A] = -ℏωB and [H, B] = ℏωA, where ω is a constant and H is the Hamiltonian of the system. The expectation value \(\left\langle A_ψ(t)=\langleψ|A| ψ〉\right.\)in a state \(|ψ〉\) such that at time t = 0, 〈A〉ψ(0) = 0 and 〈B〉ψ(0) = i, is
1
sin(ωt)
2
sinh(ωt)
3
cos(ωt)
4
cosh(ωt)