Bose-Einstein condensation in finite one-dimensional homogeneous system of noninteracting bosons

The process of condensation of the ideal Bose gas, the volume whereof is limited by the vessel walls in the form of the rectangular parallelepiped with the square foundation (the l - square side) and the L - height under the condition of the L >> l is studied. It is shown that the process of condensation both within the frames of the Bose-Einstein statistics and within the frames of the boson canonic ensemble statistics by realizing the N(l/L)4 << 1, where N constitutes the gas particles complete number, is of the one-dimensional character. The process by the N(l/L)4 >> 1 in the sense of the particles number average values in the condensate becomes the three-dimensional one, however the function of the particles number distribution in the condensate in the boson canonic ensemble statistics retains the specificity of the one-dimensional system by all N