K. Datta

Eigenvalues of λx2m anharmonic oscillators

The ground state as well as excited energy levels of the generalized anharmonic oscillator defined by the Hamiltonian Hm = − d2/dx2+x2+ λx2m, m = 2,3, …, have been calculated nonperturbatively using the Hill determinants. For the λx4 oscillator, the ground state eigenvalues, for various values of λ, have been compared with the Borel‐Pade sum of the asymptotic perturbation series for the problem. The agreement is excellent. In addition, we present results for some excited states for m = 2 as well as the ground and the first even excited states for m = 3 and 4. The behaviour of all the energy levels with respect to the coupling parameter shows a qualitative similarity to the ground state of the λx4 oscillator. Thus the results are model independent, as is to be expected from the WKB approximation. Our results also satisfy the scaling property that en(m)(λ)/λ1/(m+1) tend to a finite limit for large λ, and always lie within the variational bounds, where available.

The generalized anharmonic oscillator in three dimensions: Exact eigenvalues and eigenfunctions

We study the generalized anharmonic oscillator in three dimensions described by the potentials of the form ∑2m+1k=1bkr 2k. An asymptotic analysis of the Schrodinger equation yields the leading asymptotic behavior of the energy eigenfunctions in terms of the dominant (m+1) coupling constants bk, m+1≤k≤2m+1. Using an ansatz which incorporates this asymptotic behavior, we reduce the eigenvalue equation to an (m+2)‐term difference equation. The corresponding Hill determinant may be made to factorize with a finite determinant as a factor if a set of constraints on the couplings is satisfied; an infinite sequence of such sets exists. The exact energy eigenvalues appear as the real roots of the finite factor of the Hill determinant; the corresponding wavefunctions are Gaussian weighted polynomials. We consider the potentials ∑31bkr 2k and ∑51bkr 2k explicitly; potentials of the form ∑2m1bjr j and ∑2m1bjr j+δ/r containing both even and odd terms are also considered. Finally, we show that this method of constructi...

Are weak vector bosons composite

AbstractRecentcern

Einstein-Podolsky-Rosen paradox, statistical locality and the time-energy uncertainty relation

p\bar p

Asymptotic series for wave functions and energy levels of doubly anharmonic oscillators

collider data on anomalousZ° events suggest, among other possibilities, a composite structure for the weak intermediate vector bosons. We present a short review of these developments and examine how far the scenario for weak interactions with such composite models of the weak vector bosons presents a viable alternative to the standard electroweak theory. In particular, we show how the scale of the dynamics underlying the composite structure is set by the magnitude of the weak mixing angle sin2θw and point out the possibility of accommodating the anomalous

Relativistic oscillator in a Bethe-Salpeter model: Nonexistence of discrete bound states

Z^ \circ - l\tilde l\gamma