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We consider three different approaches to analyze the quantum mechanicalproblems in multi-well potentials:  i) the standard matrix diagonalization technique in the basis sets ofharmonic oscillator eigenfunctions or plain waves;  ii) the spectral method, which allows to reconstruct the spectrum andstationary functions based on the time-dependent solution of the Schr\"odingerequation;  iii) approximations with exact solutions obtained by the supersymmetricquantum mechanics technique.  The latter approach proves to be the most promising as it gives a uniquepossibility to include the specific multi-well features of the problem directlyin the calculation procedure.

Alternative approaches to the description of quantum dynamics in multi-well potentials