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It is well known that string theory generates the idea of higher dimensionalspacetime instead of the (3+1) dimensions, in which we seem to live. Itindicates that the extra space dimensions may remain curled up into very smallspace. In this paper, we study quantum mechanical scattering in presence ofextra compact space dimension in the hope of devising a method to get a clue tothe presence of extra space dimension. We consider a simplified model ofscattering, in which a beam of free particles is scattered due to a onedimensional Dirac-delta potential in presence of an extra compact spacedimension. We find that the incident, reflected and transmitted probabilitycurrent densities of the particles contain the information of the extradimension. Thus, by measuring experimentally the reflected and transmittedprobability current densities of the particles, we may confirm the presence ofextra dimension. We also show that the idea of compactification of the extradimensions gives rise to the quantization of the energy values of the freeparticles. So, by measuring the quantized energy values of the scattered freeparticles, we may again confirm the presence of extra dimensions. We alsodiscuss briefly, how the extra compact space dimensions can be detected if thescattering process is performed in (9+1) dimensions, in which six spacedimensions are compact.

Study of quantum mechanical scattering in presence of an extra compact space dimension