ps5 - Physics 880.06 Problem Set 5 Due Tuesday May 17 by...

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Unformatted text preview: Physics 880.06: Problem Set 5 Due Tuesday, May 17 by 11:59 P. M. 1. Consider the Ginzburg-Landau differential equation for ψ as applied to an order parameter ψ which varies in only one spatial direction, say z . If there is no vector potential, this differential equation can be written αψ + β | ψ | 2 ψ − ¯ h 2 2 m ∗ ψ ′′ ( z ) = 0 , (1) where the primes denote differentiation with respect to z. (a). Assume that α < 0 (as expected for T < T c . Show that one solution of this differential equation is ψ ( x ) = ψ tanh( z/z ) , (2) for a suitable choice of ψ and z . Also, find ψ and z in terms of the coefficients of the differential equation. Now we will apply this result to a semi-infinite superconductor occu- pying the half-space z > 0. We imagine that the region z < 0 is occupied by some non-superconducting material, and that ψ satisfies the boundary conditions ψ ( z = 0) = 0, ψ ( z → ∞ ) = ψ ....
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ps5 - Physics 880.06 Problem Set 5 Due Tuesday May 17 by...

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