What is the Significance of Sturm Liouville Theory in Quantum Mechanics?

[QMrocks]

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

 

[selfAdjoint]

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.