Improved 3-D quantum mechanical models of ion movements in a cylindrical ion-channel

Three dimensional (3-D) quantum mechanical models of ion movements in a cylindrical ion-channel, based on a steady state Schrodinger equation in a single particle system and in a time independent field, ore improved in this study. The improved models elucidate that: ions, going through a cylindrical channel, travel in the longitudinal (x) direction and wave as well as are free and trapped in an infinite deep potential energy web in the transversal (r and θ) directions. A quantum mechanical model of a single channel current can be derived from the model of ions´ movements in the longitudinal (x) direction. Experimental data of a single channel current can be parameterly fitted well with the model. The ions´ radical waves obey Bessel functions of the first kind of order I with a parameter k_n and it has a solution: R(r)=B J₁ (r k_n), where a is a constant, n=1, 2, 3, ..., and 0, 1, 2, 3, ... . The highest probability that an ion con be found In a cross section within a cylindrical ion-channel is on or close to the longitudinal axis according to the principle of the minimum energy state. The ions´ angular waves are: Θ(θ)=c ₁ exp(110)-c₂ exp(-110), where, c₁ and c₂ are constants, and l=0, 1, 2, 3 ... . These results are consistent with the previous results obtained from 3-D quantum mechanical models of ion movements in a cuboidal ion-channel and those macroscopic descriptions represented with classic theory of fluid dynamics