Undergrad Spin Offsetting Charge: How Electrons Balance Out

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Two electrons can exist close together if they have opposite spins, but this does not negate the electromagnetic repulsion between them. The wave function for electrons with anti-parallel spins is higher in energy compared to those with parallel spins, leading to a tendency for electrons to avoid each other due to spin correlation. In superconductivity, however, electrons can pair up, forming Cooper pairs that exhibit unique properties. This pairing allows them to overcome the usual repulsion and move through a lattice without resistance. The discussion highlights the complex interplay between spin, energy states, and electromagnetic forces in quantum physics.
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As I understand, two electrons may be found (close) together providing they are of opposite spin. How does this occur ? How does the character of opposite spin offset the impact of the electromagnetic force repelling these two particles of the same charge ?
 
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Cobalt101 said:
How does this occur ? How does the character of opposite spin offset the impact of the electromagnetic force repelling these two particles of the same charge ?
It doesn't. The result is that the wave function for two electrons with anti-parallel spin has a higher energy than the corresponding wave function with parallel spins, where the electrons will avoid each other because of spin correlation.
 
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DrClaude said:
It doesn't. The result is that the wave function for two electrons with anti-parallel spin has a higher energy than the corresponding wave function with parallel spins, where the electrons will avoid each other because of spin correlation.
How about under superconductivity conditions ? In which electrons "pair up" ?
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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