2体の粒子の梯子模型における固有値の数値解II ; Numerical Solutions of the Eigenvalue Problem in the Ladder Model II

A. JOSEPH

The method of self-adjoint ladder operators, developed in Parts I and II, is applied to the solution of the generalized angular-momentum problem. This reveals many interesting aspects of this approach to eigenvalue problems and, in particular, its relationship to addition of angular momentum. The complete set of irreducible unitary representations of the underlying algebra is obtained and also the corresponding Clebsch-Gordan (Wigner) coefficients for the addition of spin and angular momentum in a space of arbitrary dimension.

Kazuhiro Sano, 佐野 和博

T. Kebukawa

It is shown that the energy eigenstate of the reduced model of Anderson-Hamiltonian proposed in a prewious paper1) is simultaneously the spin eigenstate. M parameters (M denotes the number of down spin electrons) are introduced in the representation of the coupled equations of which solutions give the energy eigenvalue. Two notes on the solution of the eigenvalue problem are presented.

Edward J. Robinson

浩志 渡辺

Mario Castagnino, Graciela Domenech, Marcelo Leonardo Levinas +1 more

Applying the doublet representation we analyze the solutions of a Hamiltonian system which has eigenstates with complex eigenvalues. The example of the Friedrichs model allows us to show how the appearance of solutions with non-Hilbert initial conditions is linked to the energy degeneration of the Hamiltonian spectrum. We discuss the difficulties of giving a physical meaning to the growing or decaying non-Hilbert solutions. We also suggest a way to circumvent the problem of the anomalous probabilities related to both complex energy eigenvalues and degeneration of the spectrum.