Acknowledging the accepted BCS Reference:
John Bardeen, Leon Neil Cooper and John Robert Schrieffer, "Theory of Superconductivity", Physical Review, Vol 28, Number 6, December 1, 1957, pages 1175-1204.
Equation 2.8 addresses a conservation of momentum condition
in terms of wave vectors k:
k1 + k2 = k1' + k2' (conservation of momentum)
But surely superconductivity is an elastic condition
also requiring conservation of energy:
k1^2 + k2^2 = k1'^2 + k2'^2 (conservation of energy)
It is noted that the linear 'conservation of momentum'
does not generate the non linear 'conservation of energy',
This superconductor elastic requirement
can be mechanistically accomplished by assuming a hexagonal lattice
which has a real and reciprocal lattice identity.
and introducing a 'g' factor such that:
g(k1 + k2) = k1' + k2' (conservation of momentum)
k1^2 + k2^2 = g(k1'^2 + k2'^2) (conservation of energy)
This superconductor mechanistic reasoning is developed in:
Superconductivity, The Structure Scale Of The Universe https://arxiv.org/abs/physics/9905007
and particularly equations 2.3.11 and 2.3.12
Richard D Saam
On Thursday, May 5, 2022 at 3:05:54 PM UTC-5, Richard D. Saam wrote:
Acknowledging the accepted BCS Reference:
John Bardeen, Leon Neil Cooper and John Robert Schrieffer, "Theory of
Superconductivity", Physical Review, Vol 28, Number 6, December 1, 1957,
pages 1175-1204.
Equation 2.8 addresses a conservation of momentum condition
in terms of wave vectors k:
k1 + k2 = k1' + k2' (conservation of momentum)
But surely superconductivity is an elastic condition
also requiring conservation of energy:
k1^2 + k2^2 = k1'^2 + k2'^2 (conservation of energy)
It is noted that the linear 'conservation of momentum'
does not generate the non linear 'conservation of energy',
This superconductor elastic requirement
can be mechanistically accomplished by assuming a hexagonal lattice
which has a real and reciprocal lattice identity.
and introducing a 'g' factor such that:
g(k1 + k2) = k1' + k2' (conservation of momentum)
k1^2 + k2^2 = g(k1'^2 + k2'^2) (conservation of energy)
This superconductor mechanistic reasoning is developed in:
Superconductivity, The Structure Scale Of The Universe
https://arxiv.org/abs/physics/9905007
and particularly equations 2.3.11 and 2.3.12
Richard D Saam
If you consider the simple 1-dimensional elastic collision of two masses,
it is easy to show that if you assume conservation of energy and also
a relativity principle (either Galilean or Einstein) that those two conditions
imply conservation of momentum. You an also show that conservation
of energy and conservation of momentum imply the relativity principle.
An argument based on quantum mechanics and special relativity gives
the same result and also shows that it is the energy-momentum 4-vector
that is the most fundamental conserved quantity.
I'm not very familiar with superconductivity theory, but I wonder if adding
a 'g' factor as you do is the correct way to account for conservation of energy.
Rich L.
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