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

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?

[KSSV]

Show us the code which you tried.

[mohammad mortezaie]

syms eb ep t V phi
H=[ep+V/2 t*phi; t*conj(phi) eb+V/2];
[E,v]=eig(H);

Answer 1

[Chunru]

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 = 

[mohammad mortezaie]

Thank you

Answer 2

[Steven Lord]

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?

[mohammad mortezaie]

Yes you ar right.

My analytical solution is not correct.

Thank you so much.