conisder

>eq1:=n=(k[f1]^3+k[f2]^3)/6/Pi^2;


> eq2:=el*V=h_bar^2/2/m*(k[f2]^2-k[f1]^2);


> eq3:=solve({eq1,eq2},{k[f1],k[f2]});

> eq4:=allvalues(eq3):

Solving this i get a very very massive result. Let me take a branch:

eq5:=subs(eq4[2],k[f1]);

I get

1/h_bar*(-(1/2*n*Pi^2*h_bar^3/el/V/m+1/2*...

consider:

assume(k[f1]>0,k[f2]>0,k[f2]>k[f1],h_bar>0,m>0);

h_bar:=1.0545e-34;m:=0.10938e-31;n[0]=1e28;


> eq1:=n=(k[f1]^3+k[f2]^3)/6/Pi^2;

> eq2:=e*V=h_bar^2/2/m*(k[f2]^2-k[f1]^2);

> solve({eq1,eq2},{k[f1],k[f2]});

in the final command i get a very messy numerical&symbolic results like

{k[f1] = 1016612041.*
(-1.*RootOf(9456017282782496601177464289*n^2*Pi^4...

consider:

assume(kf2>0,q<kf2,q>0);

(PIECEWISE([0, -ln(q)+ln(kf2) < 0],[1, otherwise]));

simplify(PIECEWISE([0, -ln(q)+ln(kf2) < 0],[1, otherwise]));

i think i shall get 1 after the simplification... but i cannot...what should i do to achieve that "simplification"

consider:

assume(kf1>0,kf2>kf1,q>kf1,q<kf2);

1/2*q*Pi^2*(ln(kf1)*kf1^2-ln(kf2)*kf2^2-ln(q)*kf2^2-arctanh(1/(kf1^2+q^2)^2*(kf1^4+q^4-6*q^2*kf1^2))*kf1^2+ln(q)*kf1^2-ln(2)*kf1^2+ln(-kf1+q)*kf1^2+ln(kf1^2-q^2)*q^2-ln(kf1-q)*q^2+2*kf1^2-2*q^2-1/2*ln((q-kf2)^2)*kf2^2+3*ln(kf2+q)*kf2^2+4*q*kf2-3*q^2*ln(kf2+q)+ln(2)*kf2^2+arctanh((kf2^4+q^4-6*kf2^2*q^2)/(kf2^2+q^2)^2)*kf2^2+ln(-q+kf2)*q^2-ln(kf2^2-q^2)*q^2-4*q*kf1-3*ln(q+kf1)*kf1^2+2*arctanh((-kf1^2+q^2...