- #1
lokofer
- 106
- 0
"sum" over Eigenvalues...
Is there any mathematical meaning or it's used in Calculus or other 2branch" of mathematics de expression:
[tex] \sum_{n} e^{-u\lambda (n) } [/tex]
where every "lambda" is just an Eigenvalue of a linear operator:
[tex] L[y]=-\lambda _{n} y [/tex]
We Physicist know it as the "partition function" and is used in Statistical Mechanics and Quantum physics...in first approximmation:
[tex] \sum_{n} e^{-u\lambda (n) } = \iint dxdpe^{-uH} [/tex]
Where all the "eigenvalues" are positive...here i would like to hear if this "approach" using integrals would be rigorous from a math point of view...:tongue2:
Is there any mathematical meaning or it's used in Calculus or other 2branch" of mathematics de expression:
[tex] \sum_{n} e^{-u\lambda (n) } [/tex]
where every "lambda" is just an Eigenvalue of a linear operator:
[tex] L[y]=-\lambda _{n} y [/tex]
We Physicist know it as the "partition function" and is used in Statistical Mechanics and Quantum physics...in first approximmation:
[tex] \sum_{n} e^{-u\lambda (n) } = \iint dxdpe^{-uH} [/tex]
Where all the "eigenvalues" are positive...here i would like to hear if this "approach" using integrals would be rigorous from a math point of view...:tongue2: