# Question on orthogonal eigenfunctions

1. Jun 15, 2010

### mt8891

in this book I have by G.L Squires. One of the questions is:

if $$\phi$$1 and $$\phi$$2 are normalized eigenfunctions corresponding to the same eigenvalue. If:
$$\int$$$$\phi$$1*$$\phi$$2 d$$\tau$$ = d

where d is real, find normalized linear combinations of $$\phi$$1 and
$$\phi$$ 2 that are orthogonal to a) $$\phi$$ 1 b) $$\phi$$1 + $$\phi$$2

the part I'm having trouble with is finding a linear combination. The book gives: c1phi1 + c2phi2 (to shorten it) as the linear combo but yeah, whats the deal with that. they give a solution for a but yeah what is going on there. whats the process involved. yes, I am basically asking for a "tutor" so to speak, so I am n0t asking for any old person to help me but someone who is willing to explain it without becoming angry that I know not of such things.

Last edited: Jun 15, 2010
2. Jun 16, 2010

### mathman

Let L be the linear combination (depends on c1 and c2). In both cases you have one (of two) equation L.L=1.
(. means dot product, which is the integral you described).

For a) the other equation is L.φ1=0.
For b) the other equation is L.(φ12)=0

You wil have in both cases two equations in two unknowns (c1 and c2).