Exchange of quantum states between coupled oscillators

Exchange of quantum states between two interacting harmonic oscillator along their evolution time is discussed. It is analyzed the conditions for such exchange starting from a generic initial state and demonstrating that the effect occurs exactly only for the particular states C0|0>+Cn|N>, which includes the interesting qubits components |0>,|1>. It is also determined the relation between the coupling constant and characteristic frequencies of the oscillators to have the complete exchange.