In this work the exchange interactions in V15 magnetic molecular nanoclusters are examined. The magnetization reversal process is investigated at various values of the exchange constant set by means of the Monte Carlo method. It is shown that the most exact agreement with experimental results of the field dependence of susceptibility is observed in the following set of exchange interaction constants in the V15 magnetic molecular nanocluster: J = 500 K, J = 150 K, J = 225 K, J1 = 50 K, J2 = 50 K. For the first time, the heat capacity shows two maxima located in close proximity of each of the three transitions from the low-spin state into the high-spin behavior.

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The Jost solutions of the Schrödinger-type equation with a polynomial energy-dependent potential on the entire real line (−∞; + ∞) are investigated. The integral representations for the Jost solutions are constructed and some properties are studied.