Approximate Isometries as an Eigenvalue Problem and Angular Momentum

K. T. Hecht

Brian P. Anderson

Y. M. Zhao, A. Arima, Joseph N. Ginocchio +1 more

We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum $J$. We show that pairs with spin $J$ are reasonable building blocks for the low-lying states. For systems with only a $J={J}_{max}$ pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular, for those with total angular momenta $I\ensuremath{\leqslant}2j$. For $I=0$ eigenstates of four fermions in a single-$j$ shell we show that there is only one nonzero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.

Feng Jian-chun

The solution of spherical function is given in the paper,and it is applied reasonably in the problem of eigenvalue of angular momentum square operator.

Marko Robnik, Luca Salasnich

After reviewing the WKB series for the Schrödinger equation we calculate the semiclassical expansion for the eigenvalues of the angular momentum operator. This is the first systematic semiclassical treatment of the angular momentum for terms beyond the leading torus approximation.

G. A. Gallup