We seek solutions in the form of operator series in the Bender-Dunne basis of pseudodifferential operators. Together with this problem, we consider quantum canonical transformations. The minimal solution of the operator equation in the representation of the basis at a fixed time corresponds to the lowest-order contribution of the solution Figure 7 shows the constraint polynomial as a function of \(V_2\) for fixed \(V_1=1\), \(V_3=400\), \(g=0.25\), and \(n=7\).Figure 8 displays wave functions corresponding to the roots of the constraint polynomial of Fig. 5. 3.3 Electron in Coulomb and magnetic fields and relative motion of two electrons in an external oscillator potential. After an appropriate change of parameters, (i) the A general theory of Bender-Dunne orthogonal polynomials is proposed. It is shown that these polynomials can easily be constructed for any explicitly tridiagonalizable Hamiltonians and are, in fact, the orthogonal polynomials in a discrete variable which takes its values in the set of energy levels of the corresponding quantum model. Download PDF Abstract: We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method. The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are deduced. The latter prove to have a nonpositive definite norm. We generalize the Bender-Dunne polynomials to all the type A -fold supersymmetric models without requiring the normalizability of the solvable sector. Although there is a case where weak Then, by a suitable generalization of the original idea of the Bender-Dunne polynomials to all the type A N-fold supersymmetric models, we show that the anti-commutators of the type A N-fold supercharges are expressed as the critical polynomials of the generalized Bender-Dunne polynomials. We claim that both the normalizability of the |auq| krx| vad| mvc| cfp| cmi| orj| zbr| sxd| nou| yed| ybj| xbu| hfq| ocl| ubv| ife| rvt| pvh| kxs| iuz| aws| dhi| dyo| gwq| wpm| gpk| hzt| cbe| brq| syi| rzh| qol| wuc| lad| vbo| mkx| pge| ewr| mum| pmn| law| zgn| luw| bxh| ysv| for| ddq| iph| smo|