![]() ![]() ![]() The validity and the numerical stability of the derived expressions are demonstrated by the systematic numerical tests for the product of six-term multiplicative operators. Furthermore, a new set of ladder operators is derived which factorize the. The closed form solution of this problem for a typical complex form of the operator product is derived and proven mathematically. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. The efficient applications of the corresponding algebraic techniques within the variational or perturbative approximations require reduction of arbitrary multiplicative combinations of the su(1,1) ladder operators to the linear combinations of the normalized products K 0 a K + b K − c. The associated QNS ladder operators are occupation number, creation and annihilation operators K 0, K +, K − that satisfy the commutation relations = ± K ± and = − 2 K 0 of the Lie algebra su(1, 1). The corresponding Schrödinger equations can be conveniently solved by algebraic methods using the so-called quasi-number states (QNS) resembling the true wave functions of the Morse oscillator. The Morse oscillator is an adequate zero-order model for describing the highly excited vibrational states and large-amplitude vibrational motion. ![]()
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