Mathematica, Bose-Einstein

[Munin]

So, I've managed to get the distribution in a decent way. Using this code;

hw = 1;
kt = 25;
n = 10000;
dist[b_] := 1/(b*Exp[hw*m/kt] - 1);
normsum[b_] := Sum[dist[b]*(m + 2)*(m + 1)/2, {m, 0, 300}]
q = FindRoot[normsum[b] == n, {b, 0.5}]
occnumber = Table[N[dist[b /. q]*(m + 2)*(m + 1)/2], {m, 0, sumlim}];
Part[occnumber, 1];
ListPlot[occnumber, PlotRange -> {0, 500}]

Now I want to plot the Energy level occupation numbers where

E=Sum[m*hw*(m+1)*(m+2)*0.5/b*Exp[m*hw/kt]-1

But, I've been unable to do so, and then of course I want to get the Heat Capacity as a function of the temperature, but I think I might be able to manage that if I get some help on this.

I've been stuck for hours, please help me!

 

[Bill Simpson]

In your code above you didn't say what value sumlim should have. I'm guessing perhaps 300 to get a reasonable plot.

Are you really saying you want to assign the value of a Sum to E==2.71828?
Or do you want to assign the value of a sum to a variable of your own?

What are you trying to Sum over? I can't see if your problem is with the Sum or the Plot until you give more information. Your Sum appears to be incomplete.

 

[Munin]

Yea, the Sum should be 300. It would be easier if I just showed you what I'm trying to do:
The thing I'm trying to do is explained in:
http://www.eg.bucknell.edu/physics/ligare/ajp_bose1.pdf"

I want to get the Heat Capacity-Plot.

I've done it in Java, now all I want to do it in Mathematica as well as I'm trying to learn the language.

 

[Bill Simpson]

If you have an extraordinarily simple and well done Java implementation that looks like and is organized just like the mathematics in the paper and you wanted to show your code then it should be a pretty simple task of replacing that line by line with Mathematica.

Often it is possible to reorganize the result and replace several lines or even whole sections with a single Mathematica function, but that may be optional.

 

[alphy]

I understand the frustration of being stuck on a problem for hours. It's great that you have managed to get the distribution in a decent way using Mathematica and the code you provided. However, it seems like you are having trouble plotting the Energy level occupation numbers and obtaining the Heat Capacity as a function of temperature.

Firstly, I would suggest breaking down your problem into smaller steps. Instead of trying to plot the Energy level occupation numbers and obtaining the Heat Capacity all at once, try tackling each step separately. For example, first try to plot the Energy level occupation numbers for a specific temperature, and then try to plot it for a range of temperatures.

Secondly, make sure your code is correct and that you are using the correct formulas and variables. In your code, you have defined "hw" and "kt" as 1 and 25, respectively. However, in your formula for Energy, you are using "m" instead of "n". Make sure you are using the correct variables in your code.

Lastly, if you are still having trouble, try reaching out to other scientists or experts in the field for help. Collaboration and seeking advice from others is a crucial aspect of scientific research. Good luck!