@acer And on plkG.mw the T9 does not plot...

at file Aud2e.mw the command plot(E(nu),nu=10..60000);#???? neither plot([Re,Im](E(nu)),nu=10..6*10^4);#????

Aud2e.mwPlanckML.mwplkG.mw

Wish you well

@acer I tried writing again E(nu):=% it dosent work

please help

@acer ok

how do I close the post?

@acer Yes it's ok, please take a look at 3 maple files where I put a question mark ("????") at the plots that are inconsistent....Aud2e.mwPlanckML.mwplkG.mw

@acer 

Yes, you are right.... that is the issue  E(0):=3.259*ec;

@dharr 

dchange2.mw

Dear Sir Professor David Harrington,

I am reaching out to seek your valuable insight and expertise concerning a research challenge I am currently, particularly in the context of a photovoltaic cell project I am working on. This quantum approach requires precise calculations and adjustments in photon-electron energy transfer that classical physics alone cannot adequately describe. Given your background in electrochemistry, I am hopeful that your experience might shed light on certain aspects of these interactions and potentially clarify my approach. I would be extremely grateful if you could review my calculations and offer your opinion on their accuracy and applicability. I initially attempted to contact you via your university email address (dharr@uvic.ca), but it appears that either this address is no longer active, perhaps due to your retirement, or that my message was filtered. If possible, could we continue this correspondence over email? My personal email is michaelvio@gmail.com, and I would be honored to communicate with you directly. Thank you very much for your time and consideration.

Regarding my slow response and the fact that I look a little bit uncertain in my paper about the Audion, or one could say the Phonon, is that I didn't find the final result.

I am much obliged for your information and advice and I developed the first step in the calculus of equations (dchange2.mw from above). One could see that the method of derivation change of variable integrated on a Time Quanta period and reverse change of variable is pertinent. 

All good,

Vio

@dharr

Thanks for the hint for solving the equation. May I ask how to change the variable from t to x? I have used subs(t=1/x,T1) and multiplay with -1/x^2 as in the composite function, it is correct but I would like to know how I could use PDEtools:-dchange for Maple to do the variable change on the original odation. T2 := -subs(t = 1/x, T1)/x^2 in a single line Maple command? I haven't completed the work, but basically the idea of integrating a differential equation with changing variable with respect of time Tq = time quanta

@Carl Love ok haw I close the question.

@Axel Vogt to change var of J as a function of (1/x0) and plot as J1(t0) where t0=1/x0 

Is it possible?

@Axel Vogt ok I undestand epsilon

I want to do the calculus of J as a function of t and plot it as J with respect of t, please!

@Axel Vogt 

I didn't understand exactly what the epsilon does. 

But I have to establish an approximation with several basic functions or, more precisely, to verify the approximation of J as a function of x, transform it into a function of t (x=1/t) as a relation (series, for example), and plot it.

J := Int(T2, x = x0 + 1.542976947*10^(-13) .. x0, epsilon = 10^(-6))

Audion1.mw

@mmcdara 

Thanks a lot, I appreciate!

@mmcdara 

T1 := diff(4.381309398*10^(-18)*Ea/(exp(Ea/(3.583986085*10^(-15))) - 1), t);

T := -subs(t = 1/x, T1)/x^2;

Int(T, x = x0 .. x0 + 1.542976947*10^(-13));

`I want to approximate`` `Int(T,x=x0.. x0+1.542976947*10^(-13)AphS1.mw) in the general case with respect to x0= please!

AphS1.mw

@mmcdara 

Please help!

supposing we guess the constant a, b, c, d, and substitute t = 1/x  can you advise me to calculus the integral below where 1/435 = 0.002298850575 after that to come back to var "t"? 

restart;
a := -1.44670357887361*10^(-7);
b := -1.049267156*10^(-9);
c := 1.890440485*10^(-12);
d := -6.233924848*10^(-16);
Ea := 0.00762014687*t + a*t^2 + b*t^3 + c*t^4 + d*t^5;
T := int(5.012764943*10^(-24)*(0.00762014687/x - 1.446703579*10^(-7)/x^2 - 1.049267156*10^(-9)/x^3 + 1.890440485*10^(-12)/x^4 - 6.233924848*10^(-16)/x^5)/(x^2*(exp(1.858333303*10^18/x - 3.528091369*10^13/x^2 - 2.558858947*10^11/x^3 + 4.610237270*10^8/x^4 - 152027.3867/(x^5)) - 1)), x = 0.002298850575 .. 0.002298850575 + 1.542976947*10^(-13));
E2 := subs(t = 435, Ea);
E3 := subs(t = 528, Ea);
E4 := subs(t = 2860, Ea);
 AphS.mw  

Can we concentrate on the general solution with coefficients that fit the equation, like the diff equation?