# What are orthogonal wavefunctions?

1. May 7, 2009

### lms_89

I know what orthogonal means (well, I know orthogonal vectors are perpendicular to each other) but how can this be applied to a wavefunction?

Thanks!

2. May 7, 2009

### HallsofIvy

In Linear Algebra, abstract vector spaces, we define an inner product that generalizes the dot product of Euclidean spaces. Two vectors are said to be "orthogonal" if and only if their inner product is 0, just as two vectors in R3 are perpendicular if and only if their dot product is 0.

You can show that something like $\int_a^b f(x)\overline{g(x)}dx$ is an "inner product". That is the kind of inner product used when you are talking about "wave functions".

3. May 7, 2009

### lms_89

Ok.. that helps a bit. Thanks for the explanation :)

4. May 7, 2009

### chroot

Staff Emeritus
Orthogonal wavefunctions represent mutually exclusive physical states.

- Warren