- #1
Konte
- 90
- 1
Hello everybody,
From a complete set of orthogonal basis vector ##|i\rangle## ##\in## Hilbert space (##i## = ##1## to ##n##), I construct and obtain a nondiagonal Hamiltonian matrix
$$
\left( \begin{array}{cccccc}
\langle1|H|1\rangle & \langle1|H|2\rangle & . &. &.& \langle1|H|n\rangle \\
\langle2|H|1\rangle & . & . &. &.&. \\
. & . & . &. &.&. \\
. & . & . &. &.&. \\
. & . & . &. &.&. \\
. & . &. &. &.& \langle n|H|n\rangle \end{array} \right)
$$
After diagonalization, I obtain diagonal ##n\times n## matrix that represent the eigenvalues of the Hamiltonian, and another ##n\times n## matrix ##V## composed of scalars that represent the eigenvectors of the same Hamiltonian.
My question is, what is the link between the scalar matrix ##V## and the complete set of orthogonal basis vector ##|i\rangle## that I choose in the beginning ?
Thank you very much everybody.
Konte
From a complete set of orthogonal basis vector ##|i\rangle## ##\in## Hilbert space (##i## = ##1## to ##n##), I construct and obtain a nondiagonal Hamiltonian matrix
$$
\left( \begin{array}{cccccc}
\langle1|H|1\rangle & \langle1|H|2\rangle & . &. &.& \langle1|H|n\rangle \\
\langle2|H|1\rangle & . & . &. &.&. \\
. & . & . &. &.&. \\
. & . & . &. &.&. \\
. & . & . &. &.&. \\
. & . &. &. &.& \langle n|H|n\rangle \end{array} \right)
$$
After diagonalization, I obtain diagonal ##n\times n## matrix that represent the eigenvalues of the Hamiltonian, and another ##n\times n## matrix ##V## composed of scalars that represent the eigenvectors of the same Hamiltonian.
My question is, what is the link between the scalar matrix ##V## and the complete set of orthogonal basis vector ##|i\rangle## that I choose in the beginning ?
Thank you very much everybody.
Konte