BCS gap equations in the quantum limit

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Abstract
It was shown that in the quantum limit where only one Landau level is occupied,Tc diverges with increasing H.It was also indcated that Tc is unaffected impurities or by a nonzero g factor, in contrast to what was indicated in Ref. 2.The authors result is due to an assumption that the DOS about a Debye width of the chemical potential is constant. This approximation is questionable sice chemical potential decrease rapidly as H increases.Here Tc is calculated as a function of H in the quantum limit for an appropriate set of parameters to understand how impurities and nonzero g factor affect the result. (AIP)