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 -