TY - JOUR
T1 - Level crossing and the space of operators commuting with the Hamiltonian
AU - Valkering, T.P.
AU - Caspers, W.J.
PY - 1973
Y1 - 1973
N2 - The space of n-dimensional hermitean matrices that commute with a given hermitean matrix A + hB, h being a real parameter, is discussed. In particular a basis in this space is constructed consisting of polynomials in h of the lowest possible total degree. The sum of the degrees of the elements of this minimal basis equals 1/2n((n-1) - q , q being the number of linearly independent linear relations between the symmetrized products of A and B of order 0,…,n − 1. These linear relations determine the values of h for which crossing occurs, the total number of crossings for each value, and in some cases the order of the different crossings. A discussion of the noncrossing rule concludes this paper.
AB - The space of n-dimensional hermitean matrices that commute with a given hermitean matrix A + hB, h being a real parameter, is discussed. In particular a basis in this space is constructed consisting of polynomials in h of the lowest possible total degree. The sum of the degrees of the elements of this minimal basis equals 1/2n((n-1) - q , q being the number of linearly independent linear relations between the symmetrized products of A and B of order 0,…,n − 1. These linear relations determine the values of h for which crossing occurs, the total number of crossings for each value, and in some cases the order of the different crossings. A discussion of the noncrossing rule concludes this paper.
U2 - 10.1016/0031-8914(73)90182-1
DO - 10.1016/0031-8914(73)90182-1
M3 - Article
SN - 0031-8914
VL - 63
SP - 113
EP - 138
JO - Physica
JF - Physica
IS - 1
ER -