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The Kratzer's potential $V(r)=g_{1}/r^{2}-g_{2}/r$ is studied in quantummechanics with a generalized uncertainty principle, which includes a minimallength $\left( \Delta X\right) _{\min}=\hbar\sqrt{5\beta}$. In momentumrepresentation, the Schr\"{o}dinger equation is a generalized Heun'sdifferential equation, which reduces to a hypergeometric and to a Heun'sequations in special cases. We explicitly show that the presence of this finitelength regularizes the potential in the range of the coupling constant $g_{1}$where the corresponding Hamiltonian is not self-adjoint. In coordinate space,we perturbatively derive an analytical expression for the bound states spectrumin the first order of the deformation parameter $\beta$. We qualitativelydiscuss the effect of the minimal length on the vibration-rotation energylevels of diatomic molecules, through the Kratzer interaction. By comparisonwith an experimental result of the hydrogen molecule, an upper bound for theminimal length is found to be of about $0.01$ \AA . We argue that the minimallength would have some physical importance in studying the spectra of suchsystems

Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle