(adsbygoogle = window.adsbygoogle || []).push({}); "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:

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# Sum over Eigenvalues

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