Regularization of ${\delta }^{\prime }$ potential in general case of deformed space with minimal length

Abstract

In general case of deformed Heisenberg algebra leading to the minimal length, we present a definition of the ${\delta }^{\prime }(x)$ potential as a linear kernel of potential energy operator in momentum representation. We find exactly the energy level and corresponding eigenfunction for ${\delta }^{\prime }(x)$ and $\delta (x)-{\delta }^{\prime }(x)$ potentials in deformed space with arbitrary function of deformation. The energy spectrum for different partial cases of deformation function is analysed.

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