4 problems

Imaginary cubic oscillator spectral conjecture. The spectrum of energies is real, discrete and bounded below. Numerical and semiclassical analysis supports this conjecture. The cla…

Strong-coupling coefficient conjecture. The terms of order $K=1$ vanish, and the coefficient of the term of order $K=3$ is

Let $g$ be the coupling parameter of the cubic Hamiltonian, and consider its eigenvalues as functions of the uniformizing variable $g^{-1/5}$. Eigenvalue continuation conjecture. T…

Let … where $\chi=g^{-4/5}$ and $g$ is the original coupling parameter. Analytic continuation conjecture. The ground state energy of $H^{\mathrm{[qc]}}$ is a real analytic function…