Convergent Iterative Solutions of Schroedinger Equation for a Generalized Double Well Potential

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential $V=\frac{g^2}{2}(x^2-1)^2(x^2+a)$. The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter $a$ are discussed.Comment: 23 pages, 7 figure

Iterative Solutions for Low Lying Excited States of a Class of Schroedinger Equation

The convergent iterative procedure for solving the groundstate Schroedinger equation is extended to derive the excitation energy and the wave function of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling $g$ is not too small.Comment: 14 pages, 4 figure

The Effect of Old Age Assistance on Retirement

Researchers have devoted considerable attention to analyzing the impact of Social Security on retirement, with mixed findings. However, Old Age Assistance (OAA), a means-tested program established at the same time, dwarfed Social Security until the 1950s and coincided with the early decline in elderly participation. In addition, OAA benefit levels were determined by the states - a key source of policy variation that is missing in the case of Social Security. I estimate the relationship between OAA benefit levels and elderly labor force participation using individual data from the 1940 and 1950 Censuses. The effect of OAA is found to be strong and implies that participation would have risen slightly instead of falling if benefits had not been raised during the 1940s. I also present evidence against the endogeneity of state benefit levels.

The Impact of Technological Change on Older Workers: Evidence from Data on Computer Use

New technologies like computers alter skill requirements. This paper explores two related effects of computers on older workers, who use computers less. The evolution of computer use in the Current Population Survey suggests that impending retirement reduces the incentive of older workers to acquire new skills. The Health and Retirement Study shows, further, that computer users retire later than non-users. This may arise because computer users choose to retire later and also because workers planning later retirement choose to acquire computer skills. Instrumental variables estimates suggest that computer use directly lowers the probability of retirement.

Eisenstein Series on Covers of Odd Orthogonal Groups

We study the Whittaker coefficients of the minimal parabolic Eisenstein series on the $n$-fold cover of the split odd orthogonal group $SO_{2r+1}$. If the degree of the cover is odd, then Beineke, Brubaker and Frechette have conjectured that the $p$-power contributions to the Whittaker coefficients may be computed using the theory of crystal graphs of type C, by attaching to each path component a Gauss sum or a degenerate Gauss sum depending on the fine structure of the path. We establish their conjecture using a combination of automorphic and combinatorial-representation-theoretic methods. Surprisingly, we must make use of the type A theory, and the two different crystal graph descriptions of Brubaker, Bump and Friedberg available for type A based on different factorizations of the long word into simple reflections. We also establish a formula for the Whittaker coefficients in the even degree cover case, again based on crystal graphs of type C. As a further consequence, we establish a Lie-theoretic description of the coefficients for $n$ sufficiently large, thereby confirming a conjecture of Brubaker, Bump and Friedberg.Comment: 62 page