[bs] Osilator Harmonik

Unduh Artikel

Matlab code :

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% Quantum mechanic I, page 138                   %             

% Computing osilation psi_v2                     %       

% Andri Husein, 27 Mei 2013                      %    

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clear all

close all

clc

hbar  = 1.054e-34;    % Plank's constant

melec = 9.1e-31;      % Mass of an electron

eVtoJ = 1.6e-19;      % Energy conversion factors eV to Joule

E0 = 13.6*eVtoJ;

delta_x = .1e-11;

x_min = -300;

x_max =  300;

dx    = (x_max - x_min)/300;

x = (x_min:dx:x_max)*delta_x; % a.u

syms y;

n = 0;

omega0  = 2*E0/hbar;

alpha0  = sqrt(melec*omega0/hbar);

N0      = sqrt(alpha0/sqrt(pi));

h0      = 1;

qu = 8;

for s=1:qu

    n=n+1;

    E(s)=(n+0.5)*E0;

    omega(s) = E(s)/hbar;  

    alpha(s) = sqrt(melec*omega(s)/hbar);   

    N(s)= sqrt(alpha(s)/((2^n)*factorial(n)*sqrt(pi)));   

    h(s) = (-1)^n*exp(y.^2)*diff(exp(-y^2),y,n);

   

end

EE       = [E0 E];

w        = [omega0 omega];

alph     = [alpha0 alpha];

Normal   = [N0 N];

Hermit   = [h0 h];

V = 0.5*melec*w(6)^2*x.^2;

for s=1:qu+1;

psi(s) = Normal(s)*Hermit(s)*exp(-y^2/2);

end

psi_1=subs(psi(1),y,alph(1)*x);

psi_2=subs(psi(2),y,alph(2)*x);

psi_3=subs(psi(3),y,alph(3)*x);

psi_4=subs(psi(4),y,alph(4)*x);

psi_5=subs(psi(5),y,alph(5)*x);

psi_6=subs(psi(6),y,alph(6)*x);

psi_7=subs(psi(7),y,alph(7)*x);

psi_8=subs(psi(8),y,alph(8)*x);

psi_9=subs(psi(9),y,alph(9)*x);

h = figure(1);

set(h,'Position',[100 100 800 500]);% frame position to display

set(gcf,'Color',[1 1 1])

T  = 0;

dt = 5e-18;

i = sqrt(-1);

photo = 0;

for t_step=1:200

    photo=photo+1;

    T = T+1;

    y1(t_step)=exp(-i*w(1)*T*dt);

    y2(t_step)=exp(-i*w(2)*T*dt);

    y3(t_step)=exp(-i*w(3)*T*dt);

    y4(t_step)=exp(-i*w(4)*T*dt);

    y5(t_step)=exp(-i*w(5)*T*dt);

    y6(t_step)=exp(-i*w(6)*T*dt);

    y7(t_step)=exp(-i*w(7)*T*dt);

    y8(t_step)=exp(-i*w(8)*T*dt);

    y9(t_step)=exp(-i*w(9)*T*dt);

   

    PSIX_1=psi_1*y1(t_step);

    PSIX_2=psi_2*y2(t_step);

    PSIX_3=psi_3*y3(t_step);

    PSIX_4=psi_4*y4(t_step);

    PSIX_5=psi_5*y5(t_step);

    PSIX_6=psi_6*y6(t_step);

    PSIX_7=psi_7*y7(t_step);

    PSIX_8=psi_8*y8(t_step);

    PSIX_9=psi_9*y9(t_step);

   

    plot(x,PSIX_1*1e-5+1,'r','LineWidth',2)

    axis([-3*1e-10 3*1e-10 0 19])

    hold on

    plot(x,PSIX_2*1e-5+3,'g','LineWidth',2)

    plot(x,PSIX_3*1e-5+5,'b','LineWidth',2)

    plot(x,PSIX_4*1e-5+7,'m','LineWidth',2)

    plot(x,PSIX_5*1e-5+9,'y','LineWidth',2)

    plot(x,PSIX_6*1e-5+11,'c','LineWidth',2)

    plot(x,PSIX_7*1e-5+13,'r','LineWidth',2)

    plot(x,PSIX_8*1e-5+15,'g','LineWidth',2)

    plot(x,PSIX_9*1e-5+17,'b','LineWidth',2)   

    plot(x,V*(19/5e-16),'k--','LineWidth',2)   

    hold off

    text(1.5*1e-10,18,sprintf('t = %5.3f fs',T*dt*1e15),'fontsize',14);

    text(-2.5*1e-10,1.4,sprintf('n = 0'),'fontsize',14);

    text(-2.5*1e-10,3.4,sprintf('n = 1'),'fontsize',14);

    text(-2.5*1e-10,5.4,sprintf('n = 2'),'fontsize',14);

    text(-2.5*1e-10,7.4,sprintf('n = 3'),'fontsize',14);

    text(-2.5*1e-10,9.4,sprintf('n = 4'),'fontsize',14);

    text(-2.5*1e-10,11.4,sprintf('n = 5'),'fontsize',14);

    text(-2.5*1e-10,13.4,sprintf('n = 6'),'fontsize',14);

    text(-2.5*1e-10,15.4,sprintf('n = 7'),'fontsize',14);

    text(-2.5*1e-10,17.4,sprintf('n = 8'),'fontsize',14);

   

    set(gca,'fontsize',14)

    xlabel('x (meter)')

    ylabel('\psi (x,t)')

    set(gca,'YTick',0:4:19)

    box off

      

M(t_step)=getframe(h);

%M=getframe(h);

%[X, map] = frame2im(M);

%imwrite(X,['fig' ,num2str(photo),'.png']);

end

movie2avi(M,'Osilator.avi', 'compression', 'none')

Referensi :

Dra. Suparmi, M.A., Ph.D, Mekanika Kuantum I, Jurusan Fisika Fakultas MIPA, Universitas Sebelas Maret, Surakarta, ISBN 978-602-99344-1-0, pages 121 - 138, Juli 2011.