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Quantization of higher hamiltonian analogues of the Painleve I and Painleve II equations with two degrees of freedom

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 نشر من قبل Bulat Suleimanov Irekovich
 تاريخ النشر 2012
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Bulat Suleimanov




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We construct a solution of an analog of the Schr{o}dinger equation for the Hamiltonian $ H_I (z, t, q_1, q_2, p_1, p_2) $ corresponding to the second equation $P_1^2$ in the Painleve I hierarchy. This solution is produced by an explicit change of variables from a solution of the linear equations whose compatibility condition is the ordinary differential equation $P_1^2$ with respect to $z$. This solution also satisfies an analog of the Schr{o}dinger equation corresponding to the Hamiltonian $ H_{II} (z, t, q_1, q_2, p_1, p_2) $ of Hamiltonian system with respect to $t$ which is compatible with $P_1^2$. A similar situation occurs for the $P_2^2$ equation in the Painleve II hierarchy.



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