How to plot wave function for finite square well? [Physics question]
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Niklas Kurz
le 10 Mar 2022
Commenté : Star Strider
le 13 Mar 2022
A question addressed to other physicist among the MATLAB community:
Considering a finite sqaure well potential:
It turns out for this certain potential a symmetric wave function can be found that fits inside
Whit constants and with the energy Eof the particle and usual physical constants.
In addition the energy has to be quantised acording to as well as
Now when I atempt plotting the piecewise wave function I don't really get continous pieces:
Ce = 1.6e-19;
scale = 1e-10;
L = 2*scale;
m = 9.109*1e-31;
h = 1.05*1e-34;
V = 100*Ce;
syms k
k = vpasolve(k*tan(L/2*k) == sqrt(2*m/h^2*V-k^2),k);
beta = k*tan(L/2*k);
dx = 0.01*scale; n = 2; x1 = -L/2*n:dx:-L/2; x2 = -L/2:dx:L/2; x3 = L/2:dx:L/2*n;
C = 1; A = 1;
psi1 = C*exp(beta*x1); psi2 = A*cos(k.*x2); psi3 = C*exp(-beta*x3);
plot(x1,psi1); hold on; plot(x2,psi2); hold on; plot(x3,psi3)
I don't right know if I messed up the physics or the code itself.
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Réponse acceptée
Star Strider
le 11 Mar 2022
I do not know what it supposed to look like, however to get a continuous plot, horizongally concatenate the respectrive row vectors —
Ce = 1.6e-19;
scale = 1e-10;
L = 2*scale;
m = 9.109*1e-31;
h = 1.05*1e-34;
V = 100*Ce;
syms k
k = vpasolve(k*tan(L/2*k) == sqrt(2*m/h^2*V-k^2),k);
beta = k*tan(L/2*k);
dx = 0.01*scale; n = 2; x1 = -L/2*n:dx:-L/2; x2 = -L/2:dx:L/2; x3 = L/2:dx:L/2*n;
C = 1; A = 1;
psi1 = C*exp(beta*x1); psi2 = A*cos(k.*x2); psi3 = C*exp(-beta*x3);
plot(x1,psi1); hold on; plot(x2,psi2); hold on; plot(x3,psi3)
figure
plot([x1,x2,x3], [psi1,psi2,psi3])
grid
.
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