are complex amplitudes and satisfy the relationship \(|c_0|^2 + |c_1|^2 = 1 \) . This proves the superposition state of qubit.
 
B.  Superposition state of an asymmetric double-well in solution: spin-boson model
         Let us consider a simplified double-well system embedded in solution by using the spin-boson model in which the spin part denotes the H-bond system and the bosonic part mimics the solvent degrees of freedom. The total Hamiltonian operator of this model is then given by