MaplePrimes - answers and comments on Question, Unable to plot an integral function containing a piecewise function

beta

acer — Fri, 09 Nov 2012 19:28:48 Z

The proc T does not know the beta that you passed to g. Perhaps you meant to pass beta as a thrid argument to T.

Also, you may have intended the first conditional (the `and) to be different (missing a minus sign?).

Lastly, you might want to reduce the accuracy for the numerical integration, so that it succeeds across more values. You may have to play with that a bit...

restart;

Delta := proc(beta) options operator, arrow; sqrt(1-1/beta^2) end proc;

T := proc(`&epsilon;`, Z, beta) options operator, arrow;
 piecewise(`&epsilon;` < Delta(beta) and -Delta(beta) < `&epsilon;`,
 2*Delta(beta)^2/(`&epsilon;`^2+(Delta(beta)^2-`&epsilon;`^2)*(2*Z^2+1)^2),
 `&epsilon;` < -Delta(beta) or Delta(beta) < `&epsilon;`,
 2*abs(`&epsilon;`)/(abs(`&epsilon;`)+sqrt(`&epsilon;`^2-Delta(beta)^2)*(2*Z^2+1)))
end proc;

g := proc(V, Z, beta) options operator, arrow;
 1/(Int(T(`&epsilon;`, Z, beta)*beta*exp(beta*(`&epsilon;`-e*V))/
(exp(beta*(`&epsilon;`-e*V))+1)^2, `&epsilon;` = -infinity .. infinity,
 ':-epsilon'=1e-4, method = _NCrule)) end proc;

e := 1;

plot('g'(V, .1, 10), V = -4 .. 4);

acer

use unapply instead of -> to define

zsy312 — Sat, 10 Nov 2012 22:07:42 Z

use unapply instead of -> to define a function:

g := unapply(1/(Int(T(`ε`, Z)*beta*exp(beta*(`ε`-e*V))/(exp(beta*(`ε`-e*V))+1)^2, `ε` = -infinity .. infinity, method = _NCrule)), V, Z, beta);

':-epsilon'=1e-5

acer — Fri, 09 Nov 2012 19:39:56 Z

Using ':-epsilon'=1e-5 I got the following plot,

acer

moreover: exp(beta*(epsilon-V)) may cause over/under flow

Axel Vogt — Fri, 09 Nov 2012 19:42:35 Z

moreover: exp(beta*(epsilon-V)) may cause over/under flow

As far as I can read the code ...

Yes, that's true, I need to add β as

Budaoy — Fri, 09 Nov 2012 23:50:42 Z

Yes, that's true, I need to add β as the 3rd parameter when define T, perhaps it will help. Thank you acer.