A set of generalized-BCS equations (GBCSEs) was recently derived from a temperature-dependent Bethe-Salpeter equation and shown to deal satisfactorily with the experimental data comprising the Tcs and the multiple gaps of a variety of high-temperature superconductors (SCs). These equations are formulated in terms of the binding energies W1(T),W2(T),… of Cooper pairs (CPs) bound via one- and more than one-phonon exchange mechanisms; they contain no direct reference to the gap/s of an SC. Applications of these equations so far were based on the observation that for elemental SCs |W01|=△0 at T = 0 inthe limit of the dimensionless BCS interaction parameterλ→0. Here △0 is the zero-temperature gap whence it follows that the binding energy of a CP bound via one-phonon exchanges at T = 0 is 2|W01|. In this note we carry out a detailed comparison between the GBCSE-based W1(T) and the BCS-based energy gap △(T) for all 0≤T≤Tcand realistic, non-vanishingly-small values of λ. Our study is based on the experimental values of Tc Debye temperature , and ?0 of several selected elements including the “bad actors” such as Pb and Hg. It is thus established that the equation for W1(T) provides a viable alternative to the BCS equation for △(T). This suggests the use of, when required, the equation for W2(T) which refers to CPs bound via two-phonon exchanges, for the larger of the two T-dependent gaps of a non-elemental SC. These considerations naturally lead one to the concept of T-dependent interaction parameters in the theory of superconductivity. It is pointed out that such a concept is needed both in the well-known approach of Suhl et al. to multi-gap superconductivity and the approach provided by the GBCSEs. Attention is drawn to diverse fields where T-dependent Hamiltonians have been fruitfully employed in the past.
Cite this paper
G. Malik and M. Llano, "Some Implications of an Alternate Equation for the BCS Energy Gap," Journal of Modern Physics, Vol. 4 No. 4, 2013, pp. 6-12. doi: 10.4236/jmp.2013.44A002.
 J. Bardeen, L. N. Cooper and J. R. Schrieffer, “Theory of Superconductivity,” Physical Review, Vol. 108, No. 5, 1957, pp. 1175-1204. doi:10.1103/PhysRev.108.1175
 G. P. Malik, “On the Equivalence of the Binding Energy of a Cooper Pair and the BCS Energy Gap: A Framework for Dealing with Composite Superconductors,” International Journal of Modern Physics B, Vol. 24, No. 9, 2010, pp. 1159-1172. doi:10.1142/S0217979210055408
 G. P. Malik, “Generalized BCS Equations: Applications,” International Journal of Modern Physics B, Vol. 24, No. 19, 2010, pp. 3701-3712.
 G. P. Malik and U. Malik, “A Study of the Thallium- and Bismuth-Based High-Temperature Superconductors in the Framework of the Generalized BCS Equations,” Journal of Superconductivity and Novel Magnetism, Vol. 24, No. 1-2, 2011, pp. 255-260. doi:10.1007/s10948-010-1009-0
 H. Suhl, B. T. Matthias and L. R. Walker, “Bardeen-Cooper-Schrieffer Theory of Super-Conductivity in the Case of Overlapping Bands,” Physical Review Letters, Vol. 3, 1959, pp. 552-554.
 C. P. Poole, “Handbook of Superconductivity,” Academic Press, San Diego, 2000, p. 48.
 D. Pines, “Superconductivity in the Periodic System,” Physical Review, Vol. 109, No. 2, 1958, pp. 280-287.
 T. Mamedov and M. de Llano, “Superconducting Pseudogap in a Boson-Fermion Model,” Journal of the Physical Society of Japan, Vol. 79, No. 4, 2010, Article ID: 044706.
 T. Mamedov and M. de Llano, “Generalized Superconducting Gap in an Anisotropic BosonFermion Mixture with a Uniform Coulomb Field,” Journal of the Physical Society of Japan, Vol. 80, No. 4, 2011, Article ID: 074718.
 G. P. Malik, “On Landau Quantization of Cooper Pairs in a Heat Bath,” Physica B: Condensed Matter, Vol. 405, No. 16, 2011, pp. 3475-3481.
 J. M. Blatt, “Theory of Superconductivity,” Academic Press, New York, 1964, p. 206.
 T. P. Sheahan, “Effective Interaction Strength in Superconductors,” Physical Review, Vol. 149, No. 1, 1966, pp. 370-377. doi:10.1103/PhysRev.149.370
 S. Weinberg, “Gauge and Global Symmetries at High Temperature,” Physical Review D, Vol. 9, No. 12, 1974, pp. 3357-3378. doi:10.1103/PhysRevD.9.3357
 A. D. Linde, “Phase Transitions in Gauge Theories and Cosmology,” Reports on Progress in Physics, Vol. 42, No. 3, 1979, pp. 390-437.
 L. Dolan and R. Jackiw, “Symmetry Behavior at Finite Temperture,” Physical Review D, Vol. 9, No. 12, 1974, pp. 3320-3341. doi:10.1103/PhysRevD.9.3320
 G. P. Malik and L. K. Pande, “Wick-Cutkosky Model in the Large-Temperature Limit,” Physical Review D, Vol. 37, No. 12, 1988, pp. 3742-3748.
 G. P. Malik, L. K. Pande and V. S. Varma, “On Solar Emission Lines,” The Astrophysical Journal, Vol. 379, 1991, pp. 788-795. doi:10.1086/170554
 G. P. Malik, R. K. Jha and V. S. Varma, “Mass Spectrum of the Temperature-Dependent Bethe-Salpeter Equation for Composites of Quarks with a Coulomb plus a Linear Kernel,” The European Physical Journal A, Vol. 2, No. 1, 1998, pp. 105-110. doi:10.1007/s100500050096
 G. P. Malik, R. K. Jha and V. S. Varma, “Quarkonium Mass Spectra from the Temperature-Dependent Bethe-Salpeter Equation with Logarithmic and Coulomb plus Square-Root Kernels,” The European Physical Journal A, Vol. 3, No. 4, 1998, pp. 373-375.
 B. T. Geilikman, “Thermal Conductivity of Super-Conductors,” Soviet Physics, Vol. 7, 1958, pp. 721-722.
 B. T. Geilikman and V. Z. Kresin, “Phonon Thermal Conductivity of Superconductors,” Soviet Physics Dolady, Vol. 3, No. 6, 1958, pp. 1161-1163.
 J. Bardeen, G. Rickayzen and L. Tewordt, “Theory of Thermal Conductivity of Superconductors,” Physical Review, Vol. 113, No. 4, 1959, pp. 982-994.