7 problems

Totient threshold conjecture. If $\varphi(M-1)/2\geq 2$, then $C_M$ does not admit a representation

Persistence conjecture. The small effect observed for the quartic potential persists for these higher-order anharmonic non-local oscillators. The conjecture is supported by numeric…

Bender–Weniger conjecture. The factorially divergent perturbation expansion of this non-Hermitian $\mathcal{PT}$-symmetric anharmonic oscillator is a Stieltjes series.

Consider the resonances of the unstable oscillators as functions of the coupling parameter $g$. Resonance-persistence conjecture. The resonances of the unstable oscillators persist…

Let $h_3(g)=-\frac{1}{2}\frac{\partial^2}{\partial q^2}+\frac{1}{2}q^2+\sqrt{g}\,q^3$ be the cubic Hamiltonian, and let $B_3(E,g)$ and $A_3(E,g)$ denote the associated perturbative…

Spectral-behavior conjecture. The spectrum of the generator of the oscillator-chain model has the same behavior, as a function of $\gamma$, as the comparison operator just describe…

Bohr–Sommerfeld quantization conjecture. The quantization condition above should describe the energy levels of the cubic Hamiltonian, but only in the ${\mathcal PT}$-symmetric case…