Normalization and quantization of Hamiltonian systems using computer algebra

The normalization of Hamiltonian systems is described, i.e., the reduction of a classical Hamilton function using canonical transformations to a simpler form called the Birkhoff–Gustavson normal form. The classical normal form is obtained according to the Born–Jordan and Weyl–McCoy rules, its quantum analogs are constructed, for which the eigenvalue problem is solved, and approximate formulas for the energy spectrum are found. For partial values of the parameters of quantum normal forms, numerical calculations of the lower energy levels were carried out using these formulas.