Abstract. The physical hypothesis that beside the electromagnetic constant c and the quantum of action ℏ there is a quantum of length ℓ is essentially used in this work. This hypothesis does not require a discrete structure for any of the spaces considered similarly to the presence of ℏ which also does not require such a discrete structure. The Schrödinger equation has been supplemented by another differential equation in which the quantum ℓ takes essential part. Based on the possibilities provided by contemporary accelerators with respect to energy, this constant has been evaluated here to be ℓ ≤ 10^-8λ₀, where λ₀ is the Compton wave length of the proton. An attempt is made to explain why thus far the quantum ℓ has not been experimentally detected. Moreover, the existing theory is not rejected but supplemented. The expected enhanced possibilities pro vided by future accelerators, and other sources of high energies should bring about an experimental reflection of this addition.

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