Hello,
I want to have a lag value of variable X (PANEL of nature), but since Matlab does not accept different matrix size variables, what should I do. Variable is 4100*1 and lag of it is 3936*1.Hello,
I want to have a lag value of variable X (PANEL of nature), but since Matlab does not accept different matrix size variables, what should I do. Variable is 4100*1 and lag of it is 3936*1. Hello,
I want to have a lag value of variable X (PANEL of nature), but since Matlab does not accept different matrix size variables, what should I do. Variable is 4100*1 and lag of it is 3936*1. lag values MATLAB Answers — New Questions

​

Hello, how can I resolve the error "Invalid operand. Variables of type "sym" cannot be combined with other models." in this code. Separately if it works for me. Thanks
d=5;%sobreoscilacion
tp=4; %tiempo pico
k=100;
syms e w
ecA=((-e*pi)/sqrt(1-e^2))-log(d)== 0;
e= vpa(solve(ecA,e)); %valor epsilon
ecB=(pi/(w*(sqrt(1-e^2))))-tp==0;
w= vpa(solve(ecB,w)); %valor ohmega
%%%%
s=tf(‘s’);
Q=((k*(w)^2)/(s^2+2*e+s+(w)^2))*exp(-tp*s);
Q_apro=pade(Q,1);Hello, how can I resolve the error "Invalid operand. Variables of type "sym" cannot be combined with other models." in this code. Separately if it works for me. Thanks
d=5;%sobreoscilacion
tp=4; %tiempo pico
k=100;
syms e w
ecA=((-e*pi)/sqrt(1-e^2))-log(d)== 0;
e= vpa(solve(ecA,e)); %valor epsilon
ecB=(pi/(w*(sqrt(1-e^2))))-tp==0;
w= vpa(solve(ecB,w)); %valor ohmega
%%%%
s=tf(‘s’);
Q=((k*(w)^2)/(s^2+2*e+s+(w)^2))*exp(-tp*s);
Q_apro=pade(Q,1); Hello, how can I resolve the error "Invalid operand. Variables of type "sym" cannot be combined with other models." in this code. Separately if it works for me. Thanks
d=5;%sobreoscilacion
tp=4; %tiempo pico
k=100;
syms e w
ecA=((-e*pi)/sqrt(1-e^2))-log(d)== 0;
e= vpa(solve(ecA,e)); %valor epsilon
ecB=(pi/(w*(sqrt(1-e^2))))-tp==0;
w= vpa(solve(ecB,w)); %valor ohmega
%%%%
s=tf(‘s’);
Q=((k*(w)^2)/(s^2+2*e+s+(w)^2))*exp(-tp*s);
Q_apro=pade(Q,1); syms, sym MATLAB Answers — New Questions

​

Does anybody knows how to select only rows and not columns? I’m trying to select all the first values of each column, is that possible?Does anybody knows how to select only rows and not columns? I’m trying to select all the first values of each column, is that possible? Does anybody knows how to select only rows and not columns? I’m trying to select all the first values of each column, is that possible? rows, columns, matrix MATLAB Answers — New Questions

​

error when appending pdfserror when appending pdfs error when appending pdfs append pdf error MATLAB Answers — New Questions

​

"MinElevationAngle" is found in the ground station object to only have line-of-sight satellites above a mask angle. How can we do that for an aircraft?"MinElevationAngle" is found in the ground station object to only have line-of-sight satellites above a mask angle. How can we do that for an aircraft? "MinElevationAngle" is found in the ground station object to only have line-of-sight satellites above a mask angle. How can we do that for an aircraft? satellitescenario, platform MATLAB Answers — New Questions

​

Using App Designer I was running my program with no breakpoints set.
Suddenly it stopped running in a place it shouldn’t so I broke out to see what’s going on and found this:

My understanding is that the open arrow signifies a place where the code has called a routine and not come back yet.
So what’s wrong with this pause this time, after it ran fine 9 times in the last 10 seconds or so?Using App Designer I was running my program with no breakpoints set.
Suddenly it stopped running in a place it shouldn’t so I broke out to see what’s going on and found this:

My understanding is that the open arrow signifies a place where the code has called a routine and not come back yet.
So what’s wrong with this pause this time, after it ran fine 9 times in the last 10 seconds or so? Using App Designer I was running my program with no breakpoints set.
Suddenly it stopped running in a place it shouldn’t so I broke out to see what’s going on and found this:

My understanding is that the open arrow signifies a place where the code has called a routine and not come back yet.
So what’s wrong with this pause this time, after it ran fine 9 times in the last 10 seconds or so? pause MATLAB Answers — New Questions

​

Hi, I am trying to read a csv files into a uitable and am having problems reading the variable names in. The csv was saved using writetable and the first few lines are here:
Idx,pos,sep1,sep2,avgsep,deltaPix
1,101.1,1799.918,1868.078,1833.998,0.769999999999
2,101.2,1801.527,1868.695,1835.111,1.88299999999
3,101.3,1802.028,1869.09,1835.559,2.3309999999
4,101.4,1801.645,1869.739,1835.692,2.46399999999
5,101.5,1802.023,1869.453,1835.738,2.50999999999

This is my code to read the file :
table=app.UItable;
C=readtable(fullpath,’VariableNamingRule’,’preserve’,’FileType’,’text’);
C=table2array(C); % Wasn’t sure if I needed this
opts = detectImportOptions(fullpath)
opts.VariableNames
ReportMessage(app,’Opened Successfully’)
table.Data=C;
Its not reading in the variable name

The opts.variablenames is showing the variable names are present
ans =

1×6 cell array

{‘Idx’} {‘pos’} {‘sep1’} {‘sep2’} {‘avgsep’} {‘deltaPix’}

and opts is:
opts =

DelimitedTextImportOptions with properties:

Format Properties:
Delimiter: {‘,’}
Whitespace: ‘bt ‘
LineEnding: {‘n’ ‘r’ ‘rn’}
CommentStyle: {}
ConsecutiveDelimitersRule: ‘split’
LeadingDelimitersRule: ‘keep’
TrailingDelimitersRule: ‘ignore’
EmptyLineRule: ‘skip’
Encoding: ‘UTF-8’

Replacement Properties:
MissingRule: ‘fill’
ImportErrorRule: ‘fill’
ExtraColumnsRule: ‘addvars’

Variable Import Properties: Set types by name using setvartype
VariableNames: {‘Idx’, ‘pos’, ‘sep1’ … and 3 more}
VariableTypes: {‘double’, ‘double’, ‘double’ … and 3 more}
SelectedVariableNames: {‘Idx’, ‘pos’, ‘sep1’ … and 3 more}
VariableOptions: Show all 6 VariableOptions
Access VariableOptions sub-properties using setvaropts/getvaropts
VariableNamingRule: ‘modify’

Any reason why the variable names aren’t being populated into the uitable?
ThanksHi, I am trying to read a csv files into a uitable and am having problems reading the variable names in. The csv was saved using writetable and the first few lines are here:
Idx,pos,sep1,sep2,avgsep,deltaPix
1,101.1,1799.918,1868.078,1833.998,0.769999999999
2,101.2,1801.527,1868.695,1835.111,1.88299999999
3,101.3,1802.028,1869.09,1835.559,2.3309999999
4,101.4,1801.645,1869.739,1835.692,2.46399999999
5,101.5,1802.023,1869.453,1835.738,2.50999999999

This is my code to read the file :
table=app.UItable;
C=readtable(fullpath,’VariableNamingRule’,’preserve’,’FileType’,’text’);
C=table2array(C); % Wasn’t sure if I needed this
opts = detectImportOptions(fullpath)
opts.VariableNames
ReportMessage(app,’Opened Successfully’)
table.Data=C;
Its not reading in the variable name

The opts.variablenames is showing the variable names are present
ans =

1×6 cell array

{‘Idx’} {‘pos’} {‘sep1’} {‘sep2’} {‘avgsep’} {‘deltaPix’}

and opts is:
opts =

DelimitedTextImportOptions with properties:

Format Properties:
Delimiter: {‘,’}
Whitespace: ‘bt ‘
LineEnding: {‘n’ ‘r’ ‘rn’}
CommentStyle: {}
ConsecutiveDelimitersRule: ‘split’
LeadingDelimitersRule: ‘keep’
TrailingDelimitersRule: ‘ignore’
EmptyLineRule: ‘skip’
Encoding: ‘UTF-8’

Replacement Properties:
MissingRule: ‘fill’
ImportErrorRule: ‘fill’
ExtraColumnsRule: ‘addvars’

Variable Import Properties: Set types by name using setvartype
VariableNames: {‘Idx’, ‘pos’, ‘sep1’ … and 3 more}
VariableTypes: {‘double’, ‘double’, ‘double’ … and 3 more}
SelectedVariableNames: {‘Idx’, ‘pos’, ‘sep1’ … and 3 more}
VariableOptions: Show all 6 VariableOptions
Access VariableOptions sub-properties using setvaropts/getvaropts
VariableNamingRule: ‘modify’

Any reason why the variable names aren’t being populated into the uitable?
Thanks Hi, I am trying to read a csv files into a uitable and am having problems reading the variable names in. The csv was saved using writetable and the first few lines are here:
Idx,pos,sep1,sep2,avgsep,deltaPix
1,101.1,1799.918,1868.078,1833.998,0.769999999999
2,101.2,1801.527,1868.695,1835.111,1.88299999999
3,101.3,1802.028,1869.09,1835.559,2.3309999999
4,101.4,1801.645,1869.739,1835.692,2.46399999999
5,101.5,1802.023,1869.453,1835.738,2.50999999999

This is my code to read the file :
table=app.UItable;
C=readtable(fullpath,’VariableNamingRule’,’preserve’,’FileType’,’text’);
C=table2array(C); % Wasn’t sure if I needed this
opts = detectImportOptions(fullpath)
opts.VariableNames
ReportMessage(app,’Opened Successfully’)
table.Data=C;
Its not reading in the variable name

The opts.variablenames is showing the variable names are present
ans =

1×6 cell array

{‘Idx’} {‘pos’} {‘sep1’} {‘sep2’} {‘avgsep’} {‘deltaPix’}

and opts is:
opts =

DelimitedTextImportOptions with properties:

Format Properties:
Delimiter: {‘,’}
Whitespace: ‘bt ‘
LineEnding: {‘n’ ‘r’ ‘rn’}
CommentStyle: {}
ConsecutiveDelimitersRule: ‘split’
LeadingDelimitersRule: ‘keep’
TrailingDelimitersRule: ‘ignore’
EmptyLineRule: ‘skip’
Encoding: ‘UTF-8’

Replacement Properties:
MissingRule: ‘fill’
ImportErrorRule: ‘fill’
ExtraColumnsRule: ‘addvars’

Variable Import Properties: Set types by name using setvartype
VariableNames: {‘Idx’, ‘pos’, ‘sep1’ … and 3 more}
VariableTypes: {‘double’, ‘double’, ‘double’ … and 3 more}
SelectedVariableNames: {‘Idx’, ‘pos’, ‘sep1’ … and 3 more}
VariableOptions: Show all 6 VariableOptions
Access VariableOptions sub-properties using setvaropts/getvaropts
VariableNamingRule: ‘modify’

Any reason why the variable names aren’t being populated into the uitable?
Thanks readmatrix, uitable, variablenames MATLAB Answers — New Questions

​

I am attempting to run MATLAB on my virtual machine. When I do so, however, MATLAB crashes with references to "vm3dgl64.dll" in the stack trace, such as the snippets below:

[ 2] 0x00007ffd5899e3fe C:Program FilesMATLABR2024abinwin64libmwfl.dll+00058366

[ 5] 0x00007ffd3fd2c5bf C:Program FilesMATLABR2024abinwin64jmi.dll+00705983

[ 6] 0x00000000583a9ead C:Program FilesMATLABR2024asysjavajrewin64jrebinserverjvm.dll+02727597

[ 11] 0x00007ffe1da848ff C:windowsSYSTEM32ntdll.dll+00674047

[ 14] 0x00007ffdca59696d C:windowsSYSTEM32vm3dgl64.dll+14903661

[ 39] 0x00007ffdea4411f0 C:windowssystem32opengl32.dll+00135664
I am using Windows Server on my VMWare virtual machine, and am attempting to run MATLAB R2022b. What can I do to resolve this issue?I am attempting to run MATLAB on my virtual machine. When I do so, however, MATLAB crashes with references to "vm3dgl64.dll" in the stack trace, such as the snippets below:

[ 2] 0x00007ffd5899e3fe C:Program FilesMATLABR2024abinwin64libmwfl.dll+00058366

[ 5] 0x00007ffd3fd2c5bf C:Program FilesMATLABR2024abinwin64jmi.dll+00705983

[ 6] 0x00000000583a9ead C:Program FilesMATLABR2024asysjavajrewin64jrebinserverjvm.dll+02727597

[ 11] 0x00007ffe1da848ff C:windowsSYSTEM32ntdll.dll+00674047

[ 14] 0x00007ffdca59696d C:windowsSYSTEM32vm3dgl64.dll+14903661

[ 39] 0x00007ffdea4411f0 C:windowssystem32opengl32.dll+00135664
I am using Windows Server on my VMWare virtual machine, and am attempting to run MATLAB R2022b. What can I do to resolve this issue? I am attempting to run MATLAB on my virtual machine. When I do so, however, MATLAB crashes with references to "vm3dgl64.dll" in the stack trace, such as the snippets below:

[ 2] 0x00007ffd5899e3fe C:Program FilesMATLABR2024abinwin64libmwfl.dll+00058366

[ 5] 0x00007ffd3fd2c5bf C:Program FilesMATLABR2024abinwin64jmi.dll+00705983

[ 6] 0x00000000583a9ead C:Program FilesMATLABR2024asysjavajrewin64jrebinserverjvm.dll+02727597

[ 11] 0x00007ffe1da848ff C:windowsSYSTEM32ntdll.dll+00674047

[ 14] 0x00007ffdca59696d C:windowsSYSTEM32vm3dgl64.dll+14903661

[ 39] 0x00007ffdea4411f0 C:windowssystem32opengl32.dll+00135664
I am using Windows Server on my VMWare virtual machine, and am attempting to run MATLAB R2022b. What can I do to resolve this issue? vm, vm3dgl64.dll, graphics, driver MATLAB Answers — New Questions

​

Hi. I am calculating the energy shifts in the Cs-133 atom due to external magnetic fields by the Zeeman effect (my code is attached). For the ground state and the D1 line I have no problem, the code works fine, the plots give as the D. Steck paper. However, when I try to do it for the D2 line, it seems that the lines of different colors are mixed, which gives incorrect results, as seen in the attached image.

In the code, I construct the Hamiltonian for each magnetic field value and diagonalize the Hamiltonian. One way I got it to work is to diagonalize the Hamiltonian symbolically and then substitute the magnetic field values. However, this method takes too long, and when I tried to add the octupolar term, it does not work. I think it is a problem in the order of the eigenvalues, but I have not been able to solve it. If someone could help me, I would be eternally grateful.
This is the result I obtain.

This is the result of the reference document. In this case, the lines of different colors are not mixed.

The reference document is attached below.
Cesium D Line Data
clc
clear variables
close all

tic

%% Constants definition

line = ‘D2’; % [Ground D1 D2]
I = 7/2; % Nuclear spin
g_I = -0.00039885395; % Nuclear g-factor
J = [1/2 3/2]; % Total angular momentum
g_J = [2.002540261 0.665900 1.33408749]; % Fine structure g-factor
mu_B = (9.27400899E-24)*1E-4; % Bohr Magneton (J/G)
hbar = 1.054E-34; % Reduced Planck’s constant (Js)
Ahfs = 2*pi*hbar*[2.2981579425E9 291.9201E6 50.28827E6]; % Magnetic Dipole Constant
Bhfs = -2*pi*hbar*0.4934E6; % Electric Quadrupole Constant 5^2 P_3/2
Chfs = 2*pi*hbar*0.560E3; % Magnetic Octupole Constant 6^2 P_3/D2
Folder = pwd;

switch line
case ‘Ground’
A = Ahfs(1);
J = J(1); % Total angular momentum
g_J = g_J(1);
BF = linspace(0,15000,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{S}_{1/2}$’;
yl = ‘$E/h$ (GHz)’;
Amp = 1E-9;
yy = [-26 26];
str = ‘Ground state’;
case ‘D1’
A = Ahfs(2);
J = J(1); % Total angular momentum
g_J = g_J(2);
BF = linspace(0,5000,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{P}_{1/2}$’;
yl = ‘$E/h$ (GHz)’;
Amp = 1E-9;
yy = [-2.5 2.5];
str = ‘D1 line’;
case ‘D2’
A = Ahfs(3);
J = J(2); % Total angular momentum
g_J = g_J(3);
BF = linspace(0,500,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{P}_{3/2}$’;
yl = ‘$E/h$ (MHz)’;
Amp = 1E-6;
yy = [-1500 1500];
str = ‘D2 line’;
otherwise
error(‘Unexpected value of state.’);
end

%%

% Get the spin operator matrices for I and J

[SxI, SyI, SzI] = espin(I);
[SxJ, SyJ, SzJ] = espin(J);

% Construct the spin operators, defined as the tensor product of the spin matrices S(I) and S(J) with
% indetity matrices 1(I) and 1(J)

Ix = kron(SxI, id(J));
Iy = kron(SyI, id(J));
Iz = kron(SzI, id(J));
Jx = kron(id(I), SxJ);
Jy = kron(id(I), SyJ);
Jz = kron(id(I), SzJ);

F_values = abs(I-J):(I+J);
degeneracies = 2*F_values + 1; % Degeneracies for each F value

%% We diagonalize the Hamiltonian symbolically and then evaluate the eigenvalues in terms of the external magnetic field
energies = zeros(length(BF), (2*I+1)*(2*J+1)); % Preallocate energy array

% Check the value of J before entering the loop
if J == 1/2
% Construct Hamiltonian for J = 1/2
HZeemanBase = A*(Ix*Jx + Iy*Jy + Iz*Jz) + …
mu_B*BF(1)*(g_I*Iz + g_J*Jz); % Use BF(1) just as a placeholder for the structure
elseif J == 3/2
% Construct Hamiltonian for J = 3/2
HZeemanBase = A*(Ix*Jx + Iy*Jy + Iz*Jz) + …
mu_B*BF(1)*(g_I*Iz + g_J*Jz) + …
(Bhfs/(2*I*(2*I-1)*J*(2*J-1)))*( 3*(Ix*Jx + Iy*Jy + Iz*Jz).^2 + (3/2)*(Ix*Jx + Iy*Jy + Iz*Jz) – (Ix.^2 + Iy.^2 + Iz.^2)*(Jx.^2 + Jy.^2 + Jz.^2) );
end

for j = 1:length(BF)
% Modify the Hamiltonian for each BF(j)
HZeeman = HZeemanBase;
% Update the Zeeman term for the current magnetic field strength
HZeeman = (Amp/(2*pi*hbar))*(HZeeman + mu_B*BF(j)*(g_I*Iz + g_J*Jz));

% Diagonalize the Hamiltonian
[eigenvectors, eigenvalues] = eig(HZeeman);

% Store the eigenvalues (energies)
energies(j, 🙂 = sort(diag(real(eigenvalues))); % Sort energies for clarity
end

% Plot levels for each F group with different colors
colors = {‘r’, ‘b’, ‘g’, ‘m’, ‘k’}; % Colors for each F group
level_start = 1; % Start index for each F group
legend_handles = []; % Store plot handles for the legend

Fig = figure;
hold on;
for f_idx = 1:length(F_values)
num_levels_in_group = degeneracies(f_idx); % Number of levels for this F
level_end = level_start + num_levels_in_group – 1; % End index for this F
h = plot(BF, energies(:, level_start:level_end), ‘LineWidth’,2, ‘Color’, colors{f_idx});
legend_handles = [legend_handles, h(1)]; % Store one handle per group
level_start = level_end + 1; % Update start index for the next F group
end

set(gca, ‘xminortick’, ‘on’, ‘TickLabelInterpreter’,’latex’,’fontsize’,18);
set(gca, ‘yminortick’, ‘on’, ‘TickLabelInterpreter’,’latex’,’fontsize’,18);
xlabel(‘$|B|$ (G)’, ‘Interpreter’, ‘latex’, ‘Fontsize’, 20);
ylabel(yl, ‘Interpreter’, ‘latex’,’Fontsize’, 20);
ylim(yy);
title(titleg,’Interpreter’, ‘latex’, ‘Fontsize’, 22);
legend_labels = arrayfun(@(f) sprintf(‘$F = %.0f$’, f), F_values, ‘UniformOutput’, false);
legend(legend_handles, legend_labels, ‘Interpreter’, ‘latex’, ‘Location’, ‘northwest’);
box on;
hold off;
Filename = sprintf(‘%s/Zeeman splitting %s.png’, Folder, str);
print(Fig, Filename, ‘-dpng’, ‘-r300’);

tocHi. I am calculating the energy shifts in the Cs-133 atom due to external magnetic fields by the Zeeman effect (my code is attached). For the ground state and the D1 line I have no problem, the code works fine, the plots give as the D. Steck paper. However, when I try to do it for the D2 line, it seems that the lines of different colors are mixed, which gives incorrect results, as seen in the attached image.

In the code, I construct the Hamiltonian for each magnetic field value and diagonalize the Hamiltonian. One way I got it to work is to diagonalize the Hamiltonian symbolically and then substitute the magnetic field values. However, this method takes too long, and when I tried to add the octupolar term, it does not work. I think it is a problem in the order of the eigenvalues, but I have not been able to solve it. If someone could help me, I would be eternally grateful.
This is the result I obtain.

This is the result of the reference document. In this case, the lines of different colors are not mixed.

The reference document is attached below.
Cesium D Line Data
clc
clear variables
close all

tic

%% Constants definition

line = ‘D2’; % [Ground D1 D2]
I = 7/2; % Nuclear spin
g_I = -0.00039885395; % Nuclear g-factor
J = [1/2 3/2]; % Total angular momentum
g_J = [2.002540261 0.665900 1.33408749]; % Fine structure g-factor
mu_B = (9.27400899E-24)*1E-4; % Bohr Magneton (J/G)
hbar = 1.054E-34; % Reduced Planck’s constant (Js)
Ahfs = 2*pi*hbar*[2.2981579425E9 291.9201E6 50.28827E6]; % Magnetic Dipole Constant
Bhfs = -2*pi*hbar*0.4934E6; % Electric Quadrupole Constant 5^2 P_3/2
Chfs = 2*pi*hbar*0.560E3; % Magnetic Octupole Constant 6^2 P_3/D2
Folder = pwd;

switch line
case ‘Ground’
A = Ahfs(1);
J = J(1); % Total angular momentum
g_J = g_J(1);
BF = linspace(0,15000,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{S}_{1/2}$’;
yl = ‘$E/h$ (GHz)’;
Amp = 1E-9;
yy = [-26 26];
str = ‘Ground state’;
case ‘D1’
A = Ahfs(2);
J = J(1); % Total angular momentum
g_J = g_J(2);
BF = linspace(0,5000,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{P}_{1/2}$’;
yl = ‘$E/h$ (GHz)’;
Amp = 1E-9;
yy = [-2.5 2.5];
str = ‘D1 line’;
case ‘D2’
A = Ahfs(3);
J = J(2); % Total angular momentum
g_J = g_J(3);
BF = linspace(0,500,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{P}_{3/2}$’;
yl = ‘$E/h$ (MHz)’;
Amp = 1E-6;
yy = [-1500 1500];
str = ‘D2 line’;
otherwise
error(‘Unexpected value of state.’);
end

%%

% Get the spin operator matrices for I and J

[SxI, SyI, SzI] = espin(I);
[SxJ, SyJ, SzJ] = espin(J);

% Construct the spin operators, defined as the tensor product of the spin matrices S(I) and S(J) with
% indetity matrices 1(I) and 1(J)

Ix = kron(SxI, id(J));
Iy = kron(SyI, id(J));
Iz = kron(SzI, id(J));
Jx = kron(id(I), SxJ);
Jy = kron(id(I), SyJ);
Jz = kron(id(I), SzJ);

F_values = abs(I-J):(I+J);
degeneracies = 2*F_values + 1; % Degeneracies for each F value

%% We diagonalize the Hamiltonian symbolically and then evaluate the eigenvalues in terms of the external magnetic field
energies = zeros(length(BF), (2*I+1)*(2*J+1)); % Preallocate energy array

% Check the value of J before entering the loop
if J == 1/2
% Construct Hamiltonian for J = 1/2
HZeemanBase = A*(Ix*Jx + Iy*Jy + Iz*Jz) + …
mu_B*BF(1)*(g_I*Iz + g_J*Jz); % Use BF(1) just as a placeholder for the structure
elseif J == 3/2
% Construct Hamiltonian for J = 3/2
HZeemanBase = A*(Ix*Jx + Iy*Jy + Iz*Jz) + …
mu_B*BF(1)*(g_I*Iz + g_J*Jz) + …
(Bhfs/(2*I*(2*I-1)*J*(2*J-1)))*( 3*(Ix*Jx + Iy*Jy + Iz*Jz).^2 + (3/2)*(Ix*Jx + Iy*Jy + Iz*Jz) – (Ix.^2 + Iy.^2 + Iz.^2)*(Jx.^2 + Jy.^2 + Jz.^2) );
end

for j = 1:length(BF)
% Modify the Hamiltonian for each BF(j)
HZeeman = HZeemanBase;
% Update the Zeeman term for the current magnetic field strength
HZeeman = (Amp/(2*pi*hbar))*(HZeeman + mu_B*BF(j)*(g_I*Iz + g_J*Jz));

% Diagonalize the Hamiltonian
[eigenvectors, eigenvalues] = eig(HZeeman);

% Store the eigenvalues (energies)
energies(j, 🙂 = sort(diag(real(eigenvalues))); % Sort energies for clarity
end

% Plot levels for each F group with different colors
colors = {‘r’, ‘b’, ‘g’, ‘m’, ‘k’}; % Colors for each F group
level_start = 1; % Start index for each F group
legend_handles = []; % Store plot handles for the legend

Fig = figure;
hold on;
for f_idx = 1:length(F_values)
num_levels_in_group = degeneracies(f_idx); % Number of levels for this F
level_end = level_start + num_levels_in_group – 1; % End index for this F
h = plot(BF, energies(:, level_start:level_end), ‘LineWidth’,2, ‘Color’, colors{f_idx});
legend_handles = [legend_handles, h(1)]; % Store one handle per group
level_start = level_end + 1; % Update start index for the next F group
end

set(gca, ‘xminortick’, ‘on’, ‘TickLabelInterpreter’,’latex’,’fontsize’,18);
set(gca, ‘yminortick’, ‘on’, ‘TickLabelInterpreter’,’latex’,’fontsize’,18);
xlabel(‘$|B|$ (G)’, ‘Interpreter’, ‘latex’, ‘Fontsize’, 20);
ylabel(yl, ‘Interpreter’, ‘latex’,’Fontsize’, 20);
ylim(yy);
title(titleg,’Interpreter’, ‘latex’, ‘Fontsize’, 22);
legend_labels = arrayfun(@(f) sprintf(‘$F = %.0f$’, f), F_values, ‘UniformOutput’, false);
legend(legend_handles, legend_labels, ‘Interpreter’, ‘latex’, ‘Location’, ‘northwest’);
box on;
hold off;
Filename = sprintf(‘%s/Zeeman splitting %s.png’, Folder, str);
print(Fig, Filename, ‘-dpng’, ‘-r300’);

toc Hi. I am calculating the energy shifts in the Cs-133 atom due to external magnetic fields by the Zeeman effect (my code is attached). For the ground state and the D1 line I have no problem, the code works fine, the plots give as the D. Steck paper. However, when I try to do it for the D2 line, it seems that the lines of different colors are mixed, which gives incorrect results, as seen in the attached image.

In the code, I construct the Hamiltonian for each magnetic field value and diagonalize the Hamiltonian. One way I got it to work is to diagonalize the Hamiltonian symbolically and then substitute the magnetic field values. However, this method takes too long, and when I tried to add the octupolar term, it does not work. I think it is a problem in the order of the eigenvalues, but I have not been able to solve it. If someone could help me, I would be eternally grateful.
This is the result I obtain.

This is the result of the reference document. In this case, the lines of different colors are not mixed.

The reference document is attached below.
Cesium D Line Data
clc
clear variables
close all

tic

%% Constants definition

line = ‘D2’; % [Ground D1 D2]
I = 7/2; % Nuclear spin
g_I = -0.00039885395; % Nuclear g-factor
J = [1/2 3/2]; % Total angular momentum
g_J = [2.002540261 0.665900 1.33408749]; % Fine structure g-factor
mu_B = (9.27400899E-24)*1E-4; % Bohr Magneton (J/G)
hbar = 1.054E-34; % Reduced Planck’s constant (Js)
Ahfs = 2*pi*hbar*[2.2981579425E9 291.9201E6 50.28827E6]; % Magnetic Dipole Constant
Bhfs = -2*pi*hbar*0.4934E6; % Electric Quadrupole Constant 5^2 P_3/2
Chfs = 2*pi*hbar*0.560E3; % Magnetic Octupole Constant 6^2 P_3/D2
Folder = pwd;

switch line
case ‘Ground’
A = Ahfs(1);
J = J(1); % Total angular momentum
g_J = g_J(1);
BF = linspace(0,15000,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{S}_{1/2}$’;
yl = ‘$E/h$ (GHz)’;
Amp = 1E-9;
yy = [-26 26];
str = ‘Ground state’;
case ‘D1’
A = Ahfs(2);
J = J(1); % Total angular momentum
g_J = g_J(2);
BF = linspace(0,5000,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{P}_{1/2}$’;
yl = ‘$E/h$ (GHz)’;
Amp = 1E-9;
yy = [-2.5 2.5];
str = ‘D1 line’;
case ‘D2’
A = Ahfs(3);
J = J(2); % Total angular momentum
g_J = g_J(3);
BF = linspace(0,500,1000); % Magnetic field vector (G)
titleg = ‘$ ^{133}mathrm{Cs} , , , 6^2 mathrm{P}_{3/2}$’;
yl = ‘$E/h$ (MHz)’;
Amp = 1E-6;
yy = [-1500 1500];
str = ‘D2 line’;
otherwise
error(‘Unexpected value of state.’);
end

%%

% Get the spin operator matrices for I and J

[SxI, SyI, SzI] = espin(I);
[SxJ, SyJ, SzJ] = espin(J);

% Construct the spin operators, defined as the tensor product of the spin matrices S(I) and S(J) with
% indetity matrices 1(I) and 1(J)

Ix = kron(SxI, id(J));
Iy = kron(SyI, id(J));
Iz = kron(SzI, id(J));
Jx = kron(id(I), SxJ);
Jy = kron(id(I), SyJ);
Jz = kron(id(I), SzJ);

F_values = abs(I-J):(I+J);
degeneracies = 2*F_values + 1; % Degeneracies for each F value

%% We diagonalize the Hamiltonian symbolically and then evaluate the eigenvalues in terms of the external magnetic field
energies = zeros(length(BF), (2*I+1)*(2*J+1)); % Preallocate energy array

% Check the value of J before entering the loop
if J == 1/2
% Construct Hamiltonian for J = 1/2
HZeemanBase = A*(Ix*Jx + Iy*Jy + Iz*Jz) + …
mu_B*BF(1)*(g_I*Iz + g_J*Jz); % Use BF(1) just as a placeholder for the structure
elseif J == 3/2
% Construct Hamiltonian for J = 3/2
HZeemanBase = A*(Ix*Jx + Iy*Jy + Iz*Jz) + …
mu_B*BF(1)*(g_I*Iz + g_J*Jz) + …
(Bhfs/(2*I*(2*I-1)*J*(2*J-1)))*( 3*(Ix*Jx + Iy*Jy + Iz*Jz).^2 + (3/2)*(Ix*Jx + Iy*Jy + Iz*Jz) – (Ix.^2 + Iy.^2 + Iz.^2)*(Jx.^2 + Jy.^2 + Jz.^2) );
end

for j = 1:length(BF)
% Modify the Hamiltonian for each BF(j)
HZeeman = HZeemanBase;
% Update the Zeeman term for the current magnetic field strength
HZeeman = (Amp/(2*pi*hbar))*(HZeeman + mu_B*BF(j)*(g_I*Iz + g_J*Jz));

% Diagonalize the Hamiltonian
[eigenvectors, eigenvalues] = eig(HZeeman);

% Store the eigenvalues (energies)
energies(j, 🙂 = sort(diag(real(eigenvalues))); % Sort energies for clarity
end

% Plot levels for each F group with different colors
colors = {‘r’, ‘b’, ‘g’, ‘m’, ‘k’}; % Colors for each F group
level_start = 1; % Start index for each F group
legend_handles = []; % Store plot handles for the legend

Fig = figure;
hold on;
for f_idx = 1:length(F_values)
num_levels_in_group = degeneracies(f_idx); % Number of levels for this F
level_end = level_start + num_levels_in_group – 1; % End index for this F
h = plot(BF, energies(:, level_start:level_end), ‘LineWidth’,2, ‘Color’, colors{f_idx});
legend_handles = [legend_handles, h(1)]; % Store one handle per group
level_start = level_end + 1; % Update start index for the next F group
end

set(gca, ‘xminortick’, ‘on’, ‘TickLabelInterpreter’,’latex’,’fontsize’,18);
set(gca, ‘yminortick’, ‘on’, ‘TickLabelInterpreter’,’latex’,’fontsize’,18);
xlabel(‘$|B|$ (G)’, ‘Interpreter’, ‘latex’, ‘Fontsize’, 20);
ylabel(yl, ‘Interpreter’, ‘latex’,’Fontsize’, 20);
ylim(yy);
title(titleg,’Interpreter’, ‘latex’, ‘Fontsize’, 22);
legend_labels = arrayfun(@(f) sprintf(‘$F = %.0f$’, f), F_values, ‘UniformOutput’, false);
legend(legend_handles, legend_labels, ‘Interpreter’, ‘latex’, ‘Location’, ‘northwest’);
box on;
hold off;
Filename = sprintf(‘%s/Zeeman splitting %s.png’, Folder, str);
print(Fig, Filename, ‘-dpng’, ‘-r300’);

toc matrix, eigenvalues, diagonalization, atomic physics MATLAB Answers — New Questions

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