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Re: Exact Solution to the double well potential problem in mathematica
Posted:
Mar 19, 2014 4:24 AM


hbar = 105*10^36; m = 96*911*10^36; a = 5*10^9; b = 5*10^10; V = 3*16*10^21; k = Sqrt[(2*m*e)/((hbar)^2)]; l = Sqrt[(2*m*(V  e))/(hbar)^2];
f[e_] = k*Cot[(k)*a]  l*Tanh[(l)*b/2] // Simplify;
Plot[f[e], {e, 0, 10^18}]
FindRoot[f[e], {e, #}, WorkingPrecision > 25] & /@ Table[est, {est, {6, 15, 35, 57, 85}*10^18}]
{{e > 5.795052681985343157761426*10^18}, {e > 1.522389834765808661449499*10^17}, {e > 3.474550534236380053861731*10^17}, {e > 5.707872905176405519130226*10^17}, {e > 8.492682781188889164140891*10^17}}
Bob Hanlon
On Sat, Mar 15, 2014 at 3:47 AM, Ragavendran Nagarajan < ragavendran.nagarajan@gmail.com> wrote:
> A little background. This is a Schrodinger equation problem to find the > energy stages e in the double well where there is a step potential inside a > infinite rectangular well. After solving the boundary conditions > analytically, I tried to solve the following program in mathematica > > hbar := 1.05*10^34; > m := 0.096*9.11*10^31; > a := 5*10^9; > b := 0.5*10^9; > V := 0.3*1.6*10^19; > k = Sqrt[(2*m*e)/((hbar)^2)]; > l = Sqrt[(2*m*(V  e))/(hbar)^2]; > Block[{e}, e /. First@Solve[k*Cot[(k)*a]  l*Tanh[(l)*b/2] == 0, e]] > > As you can see since the values of the constants are very small, I am > getting a lot of errors and I am not sure how to get the solution. > > Please let me know if there is a way to solve this equation using > Mathematica. I have to submit this assignment in a couple of days, so I > wold be really really grateful if you guys can show me the way to solve > this. > > Thanks for your time > > Raga > >



