6 problems

Let $H$ be a PT-invariant Hamiltonian, and suppose that PT symmetry is unbroken, meaning that the energy eigenstates of $H$ are also eigenstates of the operator $PT$. Reality conje…

Let $A_1,\dots,A_N$ be bounded non-Hermitian operators with real spectra in a Hilbert space $\mathcal{H}$. For each $k$, let $A_k^*$ denote the adjoint of $A_k$ in $\mathcal{H}$. A…

Consider the eigenvalue problem … where $H=-\frac{d^2}{dx^2}-(ix)^3$ acts on the real line. Bessis's conjecture. All eigenvalues of $H$ are real and positive. This is a conjecture…

Let $\mathcal{H}_\varepsilon=-\partial_x^2-\partial_y^2+V_\varepsilon(x,y)$ be the non-Hermitian two-dimensional Schrödinger operator associated with a suitably chosen function…

Let $Q(t)$ be an observable operator in the infinite-dimensional Hilbert-space limit, and consider the “previous Eon” with $t<0$. The ghost-supporting spurious subspace is the subs…

Let the non-Hermitian $\mathcal{PT}$-symmetric operator studied in the paper have parameter $\varepsilon$, and distinguish its continuous spectrum from any other spectral component…