In[]:=
Integrate[V/(2Pi^2)*(2m/ℏ^2)^(3/2)*ϵ^(1/2),{ϵ,0,ϵf}]
Out[]=
2
2
V
3/2
(mϵf)
3
2
π
3
ℏ
In[]:=
Solve
2
2
V
3/2
(mϵf)
3
2
π
3
ℏ
==Ntot,ϵf
Out[]=
{{ϵfRoot[-9
2
Ntot
4
π
6
ℏ
+8
3
m
2
V
3
#1
&,1]}}
In[]:=
Reduce[-9
2
Ntot
4
π
6
ℏ
+8
3
m
2
V
3
ϵf
==0,ϵf]//FullSimplify
Out[]=
2mϵf
2/3
3
4/3
π
2/3
Ntot
V
2
ℏ
In[]:=
Solve2mϵf
2/3
3
4/3
π
2/3
Ntot
V
2
ℏ
,ϵf
Out[]=
{{ϵfRoot[-9
2
Ntot
4
π
6
ℏ
+8
3
m
2
V
3
#1
&,1]}}