Vremenski nezavisna Sredingerova jednacina za linearni harmonijski oscilator (svojstveni problem, karakteristicna jednacina) ima formu:
![](https://static.elitesecurity.org/tex/8c90e0b43a25a669d7abe2671bdb9afb.png)
odnosno
![](https://static.elitesecurity.org/tex/73840f1b8b04015a492c342ffe8eaf2b.png)
![](https://static.elitesecurity.org/tex/cc017a1b7df290bf8c5b20d66e287513.png)
Ova jednacina prvi put se pojavila u problemu oscilovanja parabolickih membrana, dakle mnogo pre pojave kvantne mehanike. Zove se Ermit - Veberova jna. Kvantna mehanika je zahtevala da se nadje resenje koje ce biti jednoznacno, neprekidno i po modulu kvadratno integrabilno.
Trazimo vezana stanja
![](https://static.elitesecurity.org/tex/ab2f392c6c66a4d9e8013d99b14b0522.png)
U gornjoj jednacini moramo uvesti smenu da sa
![](https://static.elitesecurity.org/tex/b032c66aa68d26c45d50420464a1285d.png)
![](https://static.elitesecurity.org/tex/b032c66aa68d26c45d50420464a1285d.png)
![](https://static.elitesecurity.org/tex/e625e13697b66f26c67ae0f4cd4731c9.png)
![](https://static.elitesecurity.org/tex/ca7e9631d84bcf0f5fbef02536fd0aaa.png)
![](https://static.elitesecurity.org/tex/658aea0d5c62e32098f377f868ac4723.png)