Different Ground State Energy in Tinkham's Superconductivity?

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SUMMARY

The discussion centers on discrepancies in calculating ground state energy in superconductivity as presented in "Introduction to Superconductivity" by Tinkham. The user calculated the ground state energy as E = ... - 2*(Δ²/V), while Tinkham's book states E = ... - (Δ²/V). The user references the equation (2/V) = Σ(1/E_k) to justify their calculation, indicating a misunderstanding of the factors involved in the energy equation. Clarification of the factor of 2 in equation (3.29b) is essential to resolve this discrepancy.

PREREQUISITES
  • Understanding of superconductivity principles
  • Familiarity with Tinkham's "Introduction to Superconductivity"
  • Knowledge of energy equations in quantum mechanics
  • Ability to manipulate mathematical equations involving summations
NEXT STEPS
  • Review Tinkham's section 3.4.2 for detailed explanations of ground state energy calculations
  • Study the implications of the equation (2/V) = Σ(1/E_k) in superconductivity contexts
  • Examine the derivation and significance of equation (3.29b) in Tinkham's text
  • Explore common errors in quantum mechanics calculations related to factors in equations
USEFUL FOR

Students and researchers in condensed matter physics, particularly those studying superconductivity and quantum mechanics, will benefit from this discussion.

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Homework Statement


In "Introduction to superconductivity" by Tinkham, in section 3.4.2 he calculates ground state energy. I get different result when I calculate it

My calculated Ground State Energy
[tex]E = ... - 2*\frac{\Delta^2}{V}[/tex]

But in the book
[tex]E = ... - \frac{\Delta^2}{V}[/tex]

Homework Equations



[tex]\frac{2}{V} = \sum\frac{1}{E_k}[/tex]

The Attempt at a Solution


My calculated Ground State Energy
[tex]E = ... - 2*\frac{\Delta^2}{V}[/tex]
because of
[tex]\frac{2}{V} = \sum\frac{1}{E_k}[/tex]
and if we insert it into energy equation a "2" will be there.
 
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There's a factor of 2 in eq (3.29b) that cancels the factor of 2 that you have.
 
fzero said:
There's a factor of 2 in eq (3.29b) that cancels the factor of 2 that you have.

Thank you fzero for your help.
But I'm not sure that my fault be there since that 2 is in nominator not in denominator.
 

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