Dimensional analysis of the SED

[aaaa202]

I have an exercise at the moment where I am supposed to put the Schrödingerin dimensionless form (the exact exercise is attached). I must admit that this idea of dimensional analysis is quite new to me. I don't understand how you can write the SED in the dimensionless form described. Therefore I could use some hints from one of you :) They introduce this new x' = x/x0. To put the SED in the given form are we then supposed to substitute x = x'x0 in the SED? If so I don't see how the h^2/2m disappears.

 

[Dickfore]

The second derivative also changes:
$$\frac{\partial^2}{\partial x^2} \stackrel{?}{=} k \, \frac{\partial^2}{\partial x'^2}$$
How is k related to x₀?

 

[aaaa202]

I guess the derivative somehow would throw a factor of 1/x0² in but I am overall unsure about what is done in this exercise.
Do we switch variables from: x-> x'/x0? In that case everything that is named x should just be changed to x' and I can't see what sense that would make. On the other hand we could subsitute x= x'x0 but I don't see that going anywhere. Can you in detail explain what the idea is?

 

[Dickfore]

I'm not here to do your homework. You are right that you get a factor of $1/x^2_0$ in front of the second derivative. Now, if you multiply by
$$\frac{m x^2_0}{\hbar^2}$$
the coefficient in front of the second derivative becomes $-1/2$, as required in the problem. You can read off what $\tilde{V}_0$ and $\tilde{E}$.

 

[aaaa202]

you are not here for my homework? No, I guess not but you are here to help me, and I think you can trust me on the fact that I have really tried to think this over but can't make sense of it:
So I ask again, in a more elaborative way, what is that is done:
Do we switch variables from x-> x'? In that way I don't see how the factor of 1/x0² comes in since you would basically just replace every x by x'? You could I suppose plug in x = x'x0 but that doesn't seem to make sense either. Can't you see the problem? A student pointed out the problem today too and the teacher agreed in a way and said something I didn't really get.
If you really don't want to help me fine, but please don't reply to my posts in future times :)

 

[Dickfore]

Please read through what has been already written carefully, instead of rambling on things that do not make sense.

 

[aaaa202]

I have! But your comments merely state that the derivative changes which throws in a factor of 1/x0². So in principle I can solve the problem yes. But I would like to understand what it is you do to obtain this. Why this aggressive attitude? I asked a question - if you don't want to help me then simply don't respond. And if things I say doesn't make sense maybe that should hint you at the fact that I don't understand the general procedure in this exercise.