Using the slowest observable in one-dimensional Markov processes to construct quasi-exactly-solvable generators with two explicit levels

Abstract The construction of Quasi-Exactly-Solvable quantum Hamiltonians, where only the first two eigenstates Φ 0 ( x ) and Φ 1 ( x ) of energies E 0 and E 1 are explicit, is revisited from the point of view of one-dimensional Markov processes satisfying detailed balance, whose generators are relat