- #1
sundriedtomato
- 14
- 0
[SOLVED] Functions, operator => eigenfunction, eigenvalue
Show, that functions
f1 = A*sin([tex]\theta[/tex])exp[i[tex]\phi[/tex]] and
f2 = B(3cos[tex]^{2}[/tex]([tex]\theta[/tex]) - 1) A,B - constants
are eigenfunctions of an operator
http://img358.imageshack.us/img358/3406/98211270ob1.jpg [Broken]
and find eigenvalues
This is what i got for the first function:
http://img391.imageshack.us/img391/4461/38657444ih2.jpg [Broken]
The next step is to solve left part of the equation, and than compare it to the right part.
The question arises, how to solve that equation?
I tried simplifying left part of an equation in mathcad, and I got
http://img391.imageshack.us/img391/1897/28095157bm3.jpg [Broken]
Next question from that part, is if I am doing it right, how to compare those parts, and answer a question - weather this function is an eigenfunction of an operator?
Thank You in advance, and I am constantly near computer and waiting for suggestions.
Homework Statement
Show, that functions
f1 = A*sin([tex]\theta[/tex])exp[i[tex]\phi[/tex]] and
f2 = B(3cos[tex]^{2}[/tex]([tex]\theta[/tex]) - 1) A,B - constants
are eigenfunctions of an operator
http://img358.imageshack.us/img358/3406/98211270ob1.jpg [Broken]
and find eigenvalues
The Attempt at a Solution
This is what i got for the first function:
http://img391.imageshack.us/img391/4461/38657444ih2.jpg [Broken]
The next step is to solve left part of the equation, and than compare it to the right part.
The question arises, how to solve that equation?
I tried simplifying left part of an equation in mathcad, and I got
http://img391.imageshack.us/img391/1897/28095157bm3.jpg [Broken]
Next question from that part, is if I am doing it right, how to compare those parts, and answer a question - weather this function is an eigenfunction of an operator?
Thank You in advance, and I am constantly near computer and waiting for suggestions.
Last edited by a moderator: