Complex eigenvalues for hermitian matrix
显示 更早的评论
I have been trying to find the eigenenergies the Hamiltonian using the eig() function
% constants and parameters
hbar = 6.58211*10^-4;
w1 = 2000/hbar;
w2 = 2001/hbar;
syms wph;
g = 120;
pump = 10;
% the hamiltonian
h = [w1-wph pump 0;
pump w1-wph g;
0 g w2];
This gives complex valued eigenenergies in terms of the parameter wph. This was expected because Matlab might be using an algorithm sue to which this happens. I also expected that when I plot these values against wph, they should be real but instead they come out to be complex valued with a fairly big imaginary part (code attached).
Can anyone explain why this is happening? The hamiltonian is hermitian and thus should have real eigenenergies which is not happening.
2 个评论
Neelesh Kumar Vij
2019-7-1
Here, I am attaching the plots:.png)
.png)
.png)
.png)
.png)
.png)
采纳的回答
I suspect it is because you lack the float precision with which to crunch those huge integers in your expressions, like 17373258711169930298161307553886039650995152377.
Why exactly are you using symbolic (as oposed to numeric) eigenvalue analysis here?
4 个评论
Neelesh Kumar Vij
2019-7-1
编辑：Neelesh Kumar Vij
2019-7-1
Why not as follows,
hbar = 6.58211*10^-4;
wph = linspace(0, 10/hbar,10000);
w1 = 2000/hbar;
w2 = 2001/hbar;
g = 120;
pump = 10;
clear eigen
for i=numel(wph):-1:1
h= [w1-wph(i) pump 0;
pump w1-wph(i) g;
0 g w2];
eigen(:,i)=eig(h)*hbar;
end
eigen=sort(eigen);
or sort the eigenvalues at the end as you see fit?
Neelesh Kumar Vij
2019-7-1
Matt J
2019-7-1
You're welcome, but please Accept-click the answer to signify that it solved your problem.
更多回答（0 个）
类别
在 帮助中心 和 File Exchange 中查找有关 Linear Algebra 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
