The Nature of the Cooper Pair - University of Liverpool
The Nature of the Cooper Pair - University of Liverpool
The Nature of the Cooper Pair - University of Liverpool
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We now want to find out if two electrons can attract in <strong>the</strong><br />
way just described, and form a bound state - a <strong>Cooper</strong> pair.<br />
A bound state refers to a wavefunction that has a finite size,<br />
like <strong>the</strong> wavefunction <strong>of</strong> an electron in an atom. This means<br />
that <strong>the</strong> value <strong>of</strong> <strong>the</strong> wavefunction falls <strong>of</strong>f to zero after some<br />
distance.<br />
In contrast, a free electron is not in a bound state. Its<br />
wavefunction may be e ikx , which has <strong>the</strong> same amplitude at<br />
any distance.<br />
Since we treat <strong>the</strong> potential as effectively spherical, we can use<br />
<strong>the</strong> same form <strong>of</strong> <strong>the</strong> Schrodinger equation as for <strong>the</strong> hydrogen<br />
atom.<br />
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