Quantum number and wave vector

[ewilibrium]

Hello!

Can you help me a question?

-The particle was describeb by 3 quantum number: n,l,m (not consider the spin).
-But in Solid books, writer often use wave vector $$\vec{k}$$ to describe state of particle. That is kx, ky and kz with 3 dimension of coordinate.

Then, what relation with 3 quantum number with 3 wave number?

 

[Galileo]

Your context is very vague, but based on what I've encountered in textbooks is that n,m,l are scaled wavenumbers, so that they can take integer values.
Normally the wavevector can take any value, but if you impose strict boundary conditions on the position (limit the position to a square well, or apply periodic boundary conditions) the allowed wavenumbers become a discrete set. For reference it is then sometimes useful to refer to the states by integers.

 

[Marco_84]

Hello!

Can you help me a question?

-The particle was describeb by 3 quantum number: n,l,m (not consider the spin).
-But in Solid books, writer often use wave vector $$\vec{k}$$ to describe state of particle. That is kx, ky and kz with 3 dimension of coordinate.

Then, what relation with 3 quantum number with 3 wave number?

You are using different basis.

The first (nlm) is the Basis where Lz is diagonal, but you cannot diagonalized Lz simoultaneusly with Px (remeber that: P|k>=K|k>).
infact [Lz,Px]=Py and so on.

They are just 2 different Representations.
It depends which kind of experiment u have to perform.

 

[ewilibrium]

Thanks you very much!
Then I can say n,l,m include posittion of the particle?

 

[Marco_84]

Thanks you very much!
Then I can say n,l,m include posittion of the particle?

On the sphere obviously. see spherical armonics.

bye marco