Normalisation has its application to make the values meaningful when they are operated using an operator .But still can't understand the usefulness of orthogonality ? Where it is used?
Sometimes it's not imposed, it's just there. The solutions to the 1D PIB are all mutually orthogonal, for example. As are the solutions to the harmonic oscillator. Other times we impose it because it's useful to use wavefunctions as a basis to describe other functions. When using H atom wavefunctions to describe more complicated atomic or molecular orbitals, for example, it is very convenient that the set of 1s, 2s, 2p, ... orbitals are all orthogonal to one another. Essentially, orthogonality of wavefunctions is useful for the same reason that orthogonality of Cartesian vectors is useful. You *could* use (1,0) and (√2,√2) as your unit vectors. But it's much easier to use (1,0) and (0,1).
How is this even filmed!? That's the real question. Great Quality and format!
Thanks! It's filmed like this: th-cam.com/video/YmvJVkyJbLc/w-d-xo.html
he's writing everything backwards on glass
I can feel the linear algebra coming, and it's scaring me...
Normalisation has its application to make the values meaningful when they are operated using an operator .But still can't understand the usefulness of orthogonality ? Where it is used?
Sometimes it's not imposed, it's just there. The solutions to the 1D PIB are all mutually orthogonal, for example. As are the solutions to the harmonic oscillator.
Other times we impose it because it's useful to use wavefunctions as a basis to describe other functions. When using H atom wavefunctions to describe more complicated atomic or molecular orbitals, for example, it is very convenient that the set of 1s, 2s, 2p, ... orbitals are all orthogonal to one another.
Essentially, orthogonality of wavefunctions is useful for the same reason that orthogonality of Cartesian vectors is useful. You *could* use (1,0) and (√2,√2) as your unit vectors. But it's much easier to use (1,0) and (0,1).
Thank you so much !
You're welcome!
i hate physical chemistry
This is great stuff man why hate