Can These Equations Be Represented in Bloch Form?

[jbowers9]

Homework Statement

Given: sin(Πx/a)e^6Πix/Na
and e^{2Πi/a(7/N+4)x}
can these equations be represented in Bloch form?[/B]

Homework Equations

Given that Bloch form can be represented as:
Ψ(x) = u(x) e^ikx[/B]

The Attempt at a Solution

sin(Πx/a)e^ikx w/n = 3
and e^ikxe^8Πix/a w/n = 7
[/B]

 

[BvU]

Hi,

Wy do you come with equations instead of Bloch forms ?

 

[jbowers9]

The course I'm taking identifies "Bloch form" as Ψ(x) = u(x) e^ikx.
I'm not sure I understand your question. My first answer I believe fills the bill, but the second one has u(x) in imaginary form and I'm not sure about it.

 

[jbowers9]

k = 2Πn/Na

 

[BvU]

A Bloch wave is of the form you give, so if you want to write the funtions given in the problem statement in such manner, you are supposed to identify $\vec k$ and $u(\vec r)$. For the first function, $\psi(\vec r) = \sin({\pi x\over a})\; e^{i {6\pi \over Na} x}$, what would be $\vec k$ ? and $u(\vec r)$ ?

 

[BvU]

$\vec k$ is a vector, but I think you almost got it !

 

[BvU]

I'm not sure I understand your question

Well, sin(Πx/a)eikx w/n = 3 looks like an equation to me, not a $\psi(\vec r)$

 

[jbowers9]

It's in one dimension. Why r vector? And what is k vector?

 

[BvU]

https://en.wikipedia.org/wiki/Bloch_wave

and yes, you can make it 1D by writing $\psi(x) = e^{ikx}$. Your job at hand is the same.