Shape of Potential & Wave Vector 'K': Explained

[photon79]

shapes of potentials!

Hi all..

1)we have,for example,rectangular, square well, well type etc potentials. How is the shape of a potential is determined? What is the shape of the nucleus potential?

2)I am unable to get the physical importence of the wave vector 'K' and K-space in band theory!

 

[Pieter Kuiper]

1) What is the shape of the nucleus potential?

In light nuclei it as approximately parabolic.

In heavy nuclei (uranium), alpha particles are often modeled as moving in a square well + Coulomb repulsion.

2)I am unable to get the physical importence of the wave vector 'K' and K-space in band theory!

Ask your teacher to explain it one more time.

 

[Kruger]

The wave vector k is identically to: abs(k)=2pi/lambda and momentum=h(bar)k. So you can think of it as the inverse of the wave length of a wave. Its more confortable to write psy(x)=exp(kx) than psy(x)=exp(2pi/lambda*x).
If we work in more dimensions k must be a vector and as you can see in the wave function lambda must therefor also be a vector. And 2pi/VECTOR seems to look strange.

You see?

 

[Claude Bile]

The k-vector gives the direction of wave propagation. The magnitude of k is proportional to the momentum of the wave, which as we know is related to the wavelength.

Claude.