A well known example in quantum mechanics is that of a finite rectangular potential well with a rectangular bump in the middle. I guess this closely approximates the "umbrella" effect of the $NH_3$ molecule.
But this potential is not solvable analytically.
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- I want to know if there is a solvable Hamiltonian known which mimics the effects of this potential - like from which one can exactly see the effect on the energy levels and the wave-functions of the width of the bump or the height of the bump or the well width on either side of the bump.