Strict non-tightness of the level-3 quantum bootstrap for a natural three-dimensional Hamiltonian, at an excited level

Daniel Keren, Ye Zhou

For the coupled three-dimensional double well $H=\frac{1}{2}|p{|}^2+2{\sum }_i(q_i^2-1{)}^2-{\sum }_{i<j}{q}_i^2{q}_j^2$ we exhibit, at the first excited energy level (and also at the ground state)…