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We consider the Dirac $\delta$-function potential problem in general case ofdeformed Heisenberg algebra leading to the minimal length. Exact bound andscattering solutions of the problem in quasiposition representation arepresented. We obtain that for some resonance energy the incident wave iscompletely reflected. We conclude that this effect is very sensitive to thechoice of the deformation function.

Scattering solution of Schr\"odinger equation with $\delta$-potential in deformed space with minimal length