 #1
happyparticle
 369
 19
 Homework Statement:

U unitary operator that commute with H.
## \psi_n \rangle## an eigenstate of H with eigenvalue ##E_n##
## \phi_n \rangle = U  \psi_n \rangle##
Thus,
## \phi_n \rangle = \sum_i \alpha_i \psi_n^i \rangle##
 Relevant Equations:
 ## \phi_n \rangle = \sum_i \alpha_i \psi_n^i \rangle##
Hi,
I'm not sure to understand what ## \phi_n \rangle = \sum_i \alpha_i \psi_n^i## means exactly or how we get it.
From the statement, I understand that ##[U,H] = 0## and ##H\psi_n \rangle = E_n\psi_n \rangle##
Also, a linear combination of all states is also an solution.
If U commutes with H then they have the same eigenstates (and same eigenvalues ?)
Thus, ##U\psi_n \rangle = E_n  \psi_n \rangle##
I have hard time to put all those things together or seeing what that really means.
Thank you
I'm not sure to understand what ## \phi_n \rangle = \sum_i \alpha_i \psi_n^i## means exactly or how we get it.
From the statement, I understand that ##[U,H] = 0## and ##H\psi_n \rangle = E_n\psi_n \rangle##
Also, a linear combination of all states is also an solution.
If U commutes with H then they have the same eigenstates (and same eigenvalues ?)
Thus, ##U\psi_n \rangle = E_n  \psi_n \rangle##
I have hard time to put all those things together or seeing what that really means.
Thank you