How to plot wave function for finite square well? [Physics question]

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.

[jessupj]

question/maybe hint: where did you get the value C=1?

[Niklas Kurz]

Yea, I'm also confused. In the notes I studies it was said amplitude is off importance (only for normalisation) however I do think it does matter as well.

Answer 1

[Star Strider]

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

.

[Niklas Kurz]

Nice Interpretation

[Star Strider]

Thank you!