@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attempted to contact you via your university email address (dharr@uvic.ca), but it appears that either this address is no longer active, perhaps due to your retirement, or that my message was filtered.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? 

Thank you very much,

I have changed some of the initial condition 

Ea := 0.00762014687*t + a*t^2 + b*t^3 + c*t^4 + d*t^5;
E1 := diff(Ea, t);
E2 := subs(t = 435, Ea);
E3 := subs(t = 528, Ea);
E4 := subs(t = 2860, Ea);

Thus the plot Ea looks like in Aph1_mm.mw

Do you think the plot "Ea" is accurate I mean most over 95% of the plot with equation 

E1 = 5.012764943*10^(-24)*Ea/(exp(Ea/(4.100527530*10^(-21))) - 1);

a is a bit lower than Optimization:-NLPSolve('J(10)(A)', A=-10..10);

[0.000140134440210983, [A = -0.000605241506177023]]

and my choice is a:=-0.000000144670357887361 to fit the plot with what I think it should look like.

@mmcdara 

I want to calculus the Time Quanta of the electron in the 1 S orbital of the Hydrogen atom thus I must have the exact value of the wave function of the electron!

You can see details at http://michaelvio.orgfree.com/T&SQ.pdf

Please advice!

electronFlux1.mw

electroSum.mw

I try to write the electron 1 S Hydrogen atom equation This is my site: http://michaelvio.orgfree.com/

Please contact me on my email at michaelvio@yahoo.com or michaelvio@gmail.com to give you all the details.

a=1/137 c= light speed E= Rythgerg energy rb is RadiusBohr and R is a distant constant that results from the Theory that is on the site.

Excellent solution!electronFlux1.mw

I want to consult with you on the calculus that I made ant for Time Quanta of the electron, please!

In the last file, I put the calculus of electron and I want to calculate the Time Quanta of the electron that must be rb/c the time between two consecutive o wave functions of the Hydrogen electron 1 S orbital with the boundary condition the velocity is c/137 all the time at radius R wave function =0 and 

in origin, the derivate is R with the norm condition int(P(r,o),r=0..R)=1

@Thomas Richard 

The attached file is elecSVL4Ps.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/elecSVL4Ps.mw .
 

Download elecSVL4Ps.mw

Please advise 

I look forward to your's opinion

eq1 := 2*m*(E + 8*Pi*epsilon/r)*f(r, t)/h^2 + R*diff(f(r, t), r $ 2)/r - diff(f(r, t), t $ 2)/(a^2*c^2) = 0;
iv1 := f(rb, 0) = 0, f(R, t) = 0, D[1](f)(0, 0) = R, D[2](f)(rb,0)=a*c;
sys := [eq1, iv1]:
Sol := pdsolve(sys, HINT=`*`);
pt := pdetest(Sol, sys);

These are the correct initial value, it works with the first 3 conditions but when I introduced the fourth iv:D[2](f)(rb,0)=a*c the compilation time exceed very much. To solve it I used Change of Var :r=rb*rho;