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Discrepancy between eigenvalues and eigenvectors derived from analytical solution and matlab code.

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Hello,
I have this matrix [ep+V/2 t*phi; t*conj(phi) eb-V/2].
The analytical solution for eigenvalues of this matrix is E=(eb+ep)/2+v*sqrt((eb-ep+V)/2+t^2*|phi|^2).
But matlab solution is different from this.
Can someone help me for solve this chalenge?

Accepted Answer

Chunru
Chunru on 23 Jul 2021
Edited: Chunru on 23 Jul 2021
First, the sign in the last element of H should be '-' rather than '+' as in your question. Second, "doc eig" command for the order of output variables. Third, make sure your analytical result is correct. Try manual simplification then. You may want to verify the symbolic expressions with some numerical values to see if they agree.
syms eb ep t V phi
H=[ep+V/2 t*phi; t*conj(phi) eb-V/2]
H = 
[v,d]=eig(H) % not [E, v]
v = 
d = 

More Answers (1)

Steven Lord
Steven Lord on 23 Jul 2021
syms eb ep t V phi
H=[ep+V/2 t*phi; t*conj(phi) eb+V/2]
H = 
[E,v]=eig(H)
E = 
v = 
Let's check if the elements in E and v satisfy the definition of the eigenvectors and eigenvalues for H.
simplify(H*E-E*v)
ans = 
The elements in E and v satisfy the definition of the eigenvectors and eigenvalues for H, so they are eigenvectors and eigenvalues of H. What did you say you expected the eigenvalues to be?
Are you sure you're not missing a ^2 somewhere in the first term under the radical symbol?

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