Question

Hi, I need a Matlab code satisfies the following question. Output should be a graph similar to a sine or cosine graph or similar to electrocardiograms (EKG/ECG) graph. Please I'd appreciate it. All love. Thanks :)

In elementary quantum mechanics, the square well is used to model the behavior of a bound particle, in which one or more forces (external potentials, interaction with other particles, etc) prevent or restrict its ability to move about. We have seen in class that the solutions to the Schrodinger equation in and around the quantum well result in a series of eigenvector wavefunctions with distinct energy levels. In this assignment, we will use MATLAB to create the system and experiment with different dimensions and barriers.

In MATLAB, model the finite square well scenario by building the Hamiltonian matrix and using the "eig" function to solve for the eigenvectors and eigenvalues. Experiment with potential barrier values of 500eV and 1000eV, and plot the resulting waveforms superimposed over the square well. What were the confined-state energy levels? What physical significance do the eigenvalues and eigenvectors have? Do some research on the Kronig-Penney model, in which a repeating series of finite square wells is used to model the behavior of particles within a crystalline material, and discuss the significance. What is different about the behavior of electrons in a single atom versus that in a solid material?

Answer 1

complete.m

x=0.01:0.01:2;

default=input('Press 1 if u want default ecg signal else press 2:\n');

if(default==1)

li=30/72;

a_pwav=0.25;

d_pwav=0.09;

t_pwav=0.16;

a_qwav=0.025;

d_qwav=0.066;

t_qwav=0.166;

a_qrswav=1.6;

d_qrswav=0.11;

a_swav=0.25;

d_swav=0.066;

t_swav=0.09;

a_twav=0.35;

d_twav=0.142;

t_twav=0.2;

a_uwav=0.035;

d_uwav=0.0476;

t_uwav=0.433;

else

rate=input('\n\nenter the heart beat rate :');

li=30/rate;

%p wave specifications

fprintf('\n\np wave specifications\n');

d=input('Enter 1 for default specification else press 2: \n');

if(d==1)

a_pwav=0.25;

d_pwav=0.09;

t_pwav=0.16;

else

a_pwav=input('amplitude = ');

d_pwav=input('duration = ');

t_pwav=input('p-r interval = ');

d=0;

end

%q wave specifications

fprintf('\n\nq wave specifications\n');

d=input('Enter 1 for default specification else press 2: \n');

if(d==1)

a_qwav=0.025;

d_qwav=0.066;

t_qwav=0.166;

else

a_qwav=input('amplitude = ');

d_qwav=input('duration = ');

t_qwav=0.166;

d=0;

end

%qrs wave specifications

fprintf('\n\nqrs wave specifications\n');

d=input('Enter 1 for default specification else press 2: \n');

if(d==1)

a_qrswav=1.6;

d_qrswav=0.11;

else

a_qrswav=input('amplitude = ');

d_qrswav=input('duration = ');

d=0;

end

%s wave specifications

fprintf('\n\ns wave specifications\n');

d=input('Enter 1 for default specification else press 2: \n');

if(d==1)

a_swav=0.25;

d_swav=0.066;

t_swav=0.09;

else

a_swav=input('amplitude = ');

d_swav=input('duration = ');

t_swav=0.09;

d=0;

end

%t wave specifications

fprintf('\n\nt wave specifications\n');

d=input('Enter 1 for default specification else press 2: \n');

if(d==1)

a_twav=0.35;

d_twav=0.142;

t_twav=0.2;

else

a_twav=input('amplitude = ');

d_twav=input('duration = ');

t_twav=input('s-t interval = ');

d=0;

end

%u wave specifications

fprintf('\n\nu wave specifications\n');

d=input('Enter 1 for default specification else press 2: \n');

if(d==1)

a_uwav=0.035;

d_uwav=0.0476;

t_uwav=0.433;

else

a_uwav=input('amplitude = ');

d_uwav=input('duration = ');

t_uwav=0.433;

d=0;

end

end

pwav=p_wav(x,a_pwav,d_pwav,t_pwav,li);

%qwav output

qwav=q_wav(x,a_qwav,d_qwav,t_qwav,li);

%qrswav output

qrswav=qrs_wav(x,a_qrswav,d_qrswav,li);

%swav output

swav=s_wav(x,a_swav,d_swav,t_swav,li);

%twav output

twav=t_wav(x,a_twav,d_twav,t_twav,li);

%uwav output

uwav=u_wav(x,a_uwav,d_uwav,t_uwav,li);

%ecg output

ecg=pwav+qrswav+twav+swav+qwav+uwav;

figure(1)

plot(x,ecg);

p_wav(x,a_pwav,d_pwav,t_pwav,li)

function [pwav]=p_wav(x,a_pwav,d_pwav,t_pwav,li)

l=li;

a=a_pwav;

x=x+t_pwav;

b=(2*l)/d_pwav;

n=100;

p1=1/l;

p2=0;

for i = 1:n

harm1=(((sin((pi/(2*b))*(b-(2*i))))/(b-(2*i))+(sin((pi/(2*b))*(b+(2*i))))/(b+(2*i)))*(2/pi))*cos((i*pi*x)/l);

p2=p2+harm1;

end

pwav1=p1+p2;

pwav=a*pwav1;

qrs_wav(x,a_qrswav,d_qrswav,li)

function [qrswav]=qrs_wav(x,a_qrswav,d_qrswav,li)

l=li;

a=a_qrswav;

b=(2*l)/d_qrswav;

n=100;

qrs1=(a/(2*b))*(2-b);

qrs2=0;

for i = 1:n

harm=(((2*b*a)/(i*i*pi*pi))*(1-cos((i*pi)/b)))*cos((i*pi*x)/l);

qrs2=qrs2+harm;

end

qrswav=qrs1+qrs2;

q_wav(x,a_qwav,d_qwav,t_qwav,li)

function [qwav]=q_wav(x,a_qwav,d_qwav,t_qwav,li)

l=li;

x=x+t_qwav;

a=a_qwav;

b=(2*l)/d_qwav;

n=100;

q1=(a/(2*b))*(2-b);

q2=0;

for i = 1:n

harm5=(((2*b*a)/(i*i*pi*pi))*(1-cos((i*pi)/b)))*cos((i*pi*x)/l);

q2=q2+harm5;

end

qwav=-1*(q1+q2);

s_wav(x,a_swav,d_swav,t_swav,li)

function [swav]=s_wav(x,a_swav,d_swav,t_swav,li)

l=li;

x=x-t_swav;

a=a_swav;

b=(2*l)/d_swav;

n=100;

s1=(a/(2*b))*(2-b);

s2=0;

for i = 1:n

harm3=(((2*b*a)/(i*i*pi*pi))*(1-cos((i*pi)/b)))*cos((i*pi*x)/l);

s2=s2+harm3;

end

swav=-1*(s1+s2);

t_wav(x,a_twav,d_twav,t_twav,li)

function [twav]=t_wav(x,a_twav,d_twav,t_twav,li)

l=li;

a=a_twav;

x=x-t_twav-0.045;

b=(2*l)/d_twav;

n=100;

t1=1/l;

t2=0;

for i = 1:n

harm2=(((sin((pi/(2*b))*(b-(2*i))))/(b-(2*i))+(sin((pi/(2*b))*(b+(2*i))))/(b+(2*i)))*(2/pi))*cos((i*pi*x)/l);

t2=t2+harm2;

end

twav1=t1+t2;

twav=a*twav1;

u_wav(x,a_uwav,d_uwav,t_uwav,li)

function [uwav]=u_wav(x,a_uwav,d_uwav,t_uwav,li)

l=li;

a=a_uwav

x=x-t_uwav;

b=(2*l)/d_uwav;

n=100;

u1=1/l

u2=0

for i = 1:n

harm4=(((sin((pi/(2*b))*(b-(2*i))))/(b-(2*i))+(sin((pi/(2*b))*(b+(2*i))))/(b+(2*i)))*(2/pi))*cos((i*pi*x)/l);

u2=u2+harm4;

end

uwav1=u1+u2;

uwav=a*uwav1;