HOW TO SOLVE TRANSCENDENTAL EQUATION

% HOW TO FIND THE VALUE OF Enle FROM GIVEN Transcendental equation

Vc=0.249;

c=3e8;

m0=0.511e6/c^2;

me1=0.067*m0;

me2=0.092*m0;

hr=6.58e-16;

r1=3.0e-9;

d=1.0e-9;

k=sqrt((2*me1*Enle)./(hr^2));

K=sqrt((2*me2*(Vc-Enle))./(hr^2));

Q=(me2/me1);

P=(1-(k*r1)*cot(k*r1));

S=(1+(K*r1)*coth(K*d));

% Transcendental equation Q*P=S

[David Goodmanson]

Hi arvind,

could you comment on what physical system these equations describe?

[Arvind Sharma]

This is a transcendental equation of Core-well system of semiconductor material. which tells about the energy of electron for ground state for n=1 and l=0;

Answer 1

[Torsten]

function main
  Enle0 = 1.0;
  Enle = fzero(@fun,Enle0)
end

function res = fun(Enle)
  Vc = 0.249;
  c = 3e8;
  m0 = 0.511e6/c^2;
  me1 = 0.067*m0;
  me2 = 0.092*m0;
  hr = 6.58e-16;
  r1 = 3.0e-9;
  d = 1.0e-9;
  k = sqrt(2*me1*Enle/hr^2);
  K = sqrt(2*me2*(Vc-Enle)/hr^2);
  Q = me2/me1;
  P = 1-(k*r1)*cot(k*r1);
  S = 1+(K*r1)*coth(K*d);
  res = Q*P-S;
end