Understanding Orthogonality in Wavefunctions

[hellomister]

Homework Statement

If you want to show two wavefunctions are orthogonal, do you have to normalize the wavefunctions first then take the integral of the product and see if they're equal to 0?

Homework Equations

n/a

The Attempt at a Solution

not really applicable. I just want a explanation.

 

[blkqi]

Nope. Orthogonality just requires the inner product to be zero.

A good visualization (though not in Hilbert space): In Euclidean 3-space (where inner product is the dot product) orthogonal vectors are perpendicular. Normalization scales vectors to the unit length. Heres the point: two vectors are perpendicular (orthogonal) regardless of their magnitude.

Normalized, orthogonal vectors have a name too: orthonormal.

 

[hellomister]

okay thank you for the help!