Goryachev–Chaplygin top in quantum mechanics

The quantum analog of the Goryachev–Chaplygin top on the basis of the Euclidean group $E(3)$ is constructed. A representation of the generators of $E(3)$ by functions of two bosch creation and annihilation operators is considered, the problem taking on its most natural form in terms of these operators. For example, the finding of the spectrum of integrals in the Fock representation reduces to finding the eigenvalues of semi-infinite tridiagonal Jacobi matrices; the equations of motion acquire a particularly simple form.