# QM and Sturm Liouville Theory

QMrocks
Can someone pls explain what is the significance of Sturm Liouville Theory to Quantum Mechanics?

Staff Emeritus
Gold Member
Dearly Missed
Sturm and Liouville in the nineteenth century introduced the technology of linear algebra into the theory of differential equations and showed the importance of eigenvalues to the solutions. This mathematical technology, as subsequently developed by Hilbert and others, is the basis for solutions in quantum theory.

QMrocks
Thanks! i was curious if understanding of this Sturm and Liouville theory is pertinent to the understanding of QM and what essence would one miss if one does not know this this...

snooper007
In QM, completeness of eigenfunctions is very important, the completeness
in Sturm and Liouville theory is also very important.

Last edited: