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. 2015 Nov 2;5:15816. doi: 10.1038/srep15816

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Arbitrary potential energy landscape of a system. When the system is in proximity of a local maximum it obeys the Hamiltonian of a RO, . In proximity of the minimum the system obeys the Hamiltonian of a HO, . Both the reversed and the harmonic oscillators can occur for a given system as it explores its local energy landscape. The corresponding classical equations for the two Hamiltonians are also indicated in the text boxes. On the left side are reported the exploding eigenstates corresponding to the imaginary part, Γ_n/2, of the eigenvalues of the RO Hamiltonian, . On the right side are shown the bounded eigenstates of the HO associated with increasing quantized energy levels, E_n, corresponding to the eigenvalues of the Hamiltonian .

Inline graphic — Arbitrary potential energy landscape of a system. When the system is in proximity of a local maximum it obeys the Hamiltonian of a RO, . In proximity of the minimum the system obeys the Hamiltonian of a HO, . Both the reversed and the harmonic oscillators can occur for a given system as it explores its local energy landscape. The corresponding classical equations for the two Hamiltonians are also indicated in the text boxes. On the left side are reported the exploding eigenstates corresponding to the imaginary part, Γ_n/2, of the eigenvalues of the RO Hamiltonian, . On the right side are shown the bounded eigenstates of the HO associated with increasing quantized energy levels, E_n, corresponding to the eigenvalues of the Hamiltonian .