= Morse oscillator
{c}
{title2=$E_n=A(n+1/2)-B(n+1/2)^2$}
The quantum Hamiltonian with kinetic energy $p^2/(2\mu)$ and <Morse potential> has bound energies of the displayed form, where $A=\hbar\omega_e$, $B=A^2/(4D_e)>0$ and $\omega_e=a\sqrt{2D_e/\mu}$. Adjacent energy differences are $A-2B(n+1)$, distinct and positive over the physical bound-level range. A finite truncation with nonzero adjacent dipole couplings therefore satisfies <connected nondegenerate transition chain generates special unitary control>. Controllability of such a truncation does not by itself prove controllability on the full space including dissociation states.
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