Answer to Question #72723 in Algebra for rudi

Question

hi , I diagonalize hamiltonian H, then I found by chance , that this basis of eigenstates is also a basis of eigenstates of another operator let's call it "O" , which means that the Hamiltonian commute with that operator , before I diagonalizing in that basis , I have H (NxN matrix ) as will as (NxN) matrix for operator "O" , when I diagonalize the matrix of operator O I found that this operator have just two eigenvalues , two eigenstates as well (no matter what N ) , when I diagonalize H I found that it have N different eigenstates where part of them match the requirement of the first eigenstate of operator "O" and other part match the requirement of the second one , I want to understand mathematically how this match happens for example why would the ground state of the Hamiltonian match the requirement of the first eigenstate of operator O , . I wish that my question was clear , I am not a mathematician

Answer 1

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