Abstract:
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.
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