Approximate energy levels and sizes of bound quantum systems

Abstract

Articles you may be interested inApproximation method for a spherical bound system in the quantum plasma Phys. Plasmas 17, 082110 (2010); 10.1063/1.3478988Approximate energy levels of bound quantum systems Am.

Bound states of oscillators in infinite and finite domains: A semiclassical study

“…Now, to express V n as a function of x n , we take recourse to the SR mentioned above, or modifications thereof, depending on the case in hand. In what follows, we consider a few situations, takingh = 1 and m = 1 2 for convenience (see also [1]). …”

“…Here we like to put forward a perturbative route and extract the asymptotic (large-coupling) behavior of energy eigenvalues and certain properties. For the quartic anharmonic oscillator problem, this was partially accomplished [1]. Some new results are obtained in this context.…”

“…a bound to which has recently been obtained [5] and (ii) the standard semiclassical requirement (SR) [1,6,7] that x p ≈ x p , unless forbidden on the ground of symmetry. However, we shall modify the SR for systems confined in (−L, L) with proper reasoning in due course.…”

“…The above UCP-based quantization scheme was first put forward by Gersch and Braden in an educational note [1]. They approximated A n in (1) by nh and provided some justifications for the choice.…”

“…Being unaware of the earlier works [1,2], we have demonstrated [3] several advantages of the scheme, including the possibility of obtaining bounds and the workability to resonant states. We also showed [4] the relationship of this scheme with a semiclassical nonlinear differential equation (NLDE) formalism developed by Orland [6,7].…”