Harmonic twofold potential

Figure 21.1 Eigenstates and energy eigenvalues of the Schrodinger equation of a rigid Dj rotor in a harmonic twofold potential for two different depths of the potential barrier (adapted from Ref [40]). Upper panel ...

The solution to the Hamiltonian of a vibration system is a Fourier series with multiple terms of frequencies being fold of that of the primary mode [30]. For example, the frequency of the secondary 2D mode should be twofold that of the primary D mode of diamond. Instead of the multi-phonon resonant scattering, Raman frequencies are the characteristics of the solution. Generally, one can measure the Raman frequency of a particular x mode as co = co o + Aco, where cOxO is the reference point from which the Raman shift Aco proceeds. The cOxo may vary with the frequency of the incident radiation and substrate conditions, but not the nature and the trends induced by the applied stimuli. By expanding the interatomic potential in a Taylor series at its equilibrium and considering the effective atomic z, one can derive the vibration frequency shift of a harmonic system,... 

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