Shape invariance and the exactness of quantum Hamilton-Jacobi formalism

Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr\"odinger equation. It was recently shown that the shape invariance, which is an integrability condition in SUSYQM formalism, can be utilized to develop an iterative algorithm to determine the quantum momentum functions. In this paper, we show that shape invariance also suffices to determine the eigenvalues in Quantum Hamilton-Jacobi Theory.Comment: Accepted for publication in Phys. Lett.

Potentials with Two Shifted Sets of Equally Spaced Eigenvalues and Their Calogero Spectrum

Motivated by the concept of shape invariance in supersymmetric quantum mechanics, we obtain potentials whose spectrum consists of two shifted sets of equally spaced energy levels. These potentials are similar to the Calogero-Sutherland model except the singular term $\alpha x^{-2}$ always falls in the transition region $-1/4 < \alpha < 3/4$ and there is a delta-function singularity at x=0.Comment: Latex, 12 pages, Figures available from Authors, To appear in Physics Letters A. Please send requests for figures to [email protected] or [email protected]

State Variation in the Hospital Costs of Gun Violence, 2010 and 2014

This brief updates the armed assault hospital cost estimates with data from 2014, the first year of full implementation of the ACA's major coverage provisions. We provide data for Arizona, Florida, Kentucky, New Jersey, North Carolina, and Wisconsin; of these, Arizona, New Jersey, North Carolina, and Wisconsin were included in our previous brief. We selected these six states based on data availability, population size, geographic representation, and participation in the ACA Medicaid expansion (table 1). The states reflect a range of decisions on Medicaid coverage: Arizona, Kentucky, and New Jersey adopted the Medicaid expansion in 2014, but Florida, North Carolina, and Wisconsin did not. Arizona had a Section 1115 demonstration waiver in place in 2010 that provided coverage to childless adults with incomes up to 100 percent of the federal poverty level (FPL). Wisconsin also had a Section 1115 demonstration waiver to extend eligibility to 200 percent of FPL, but enrollment for the program was capped as of October 2009. In 2014, Wisconsin used state funds to provide eligibility to childless adults with incomes up to 100 percent of FPL and removed the enrollment cap. Most importantly, all six states have complete data for the analysis from the Healthcare Cost and Utilization Project, described later in this brief

The motion of two identical masses connected by an ideal string symmetrically placed over a corner

We introduce a novel, two-mass system that slides up an inclined plane while its center of mass moves down. The system consists of two identical masses connected by an ideal string symmetrically placed over a corner-shaped support. This system is similar to a double-cone that rolls up an inclined set of V-shaped rails. We find the double-cone's motion easy to demonstrate but difficult to analyze. Our example here is more straightforward to follow, and the experimental observations are in good agreement with the theoretical predictions.Comment: 10 pages, 7 figures; Accepted for publication in American Journal of Physic

Unintended consequences of imprecise Notation -- an example from mechanics

We present a conundrum that results from the imprecise use of notation for partial derivatives. Taking an example from mechanics, we show that lack of proper care in representing partial derivatives in Lagrangian and Hamiltonian formulations paradoxically leads to two different values for the time derivative of the canonical momentum. This problem also exists in other areas of physics, such as thermodynamics

Barn and Pole paradox: revisited

We present two different paradoxes related to the length contraction in special relativity and explain their resolution.Comment: 7 pages, 6 figures. To appear in Physics Education, IOP Scienc

Exactly solvable models of supersymmetric quantum mechanics and connection to spectrum generating algebra

For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess spectrum generating algebras and are hence solvable by an independent group theoretic method. In this paper, we demonstrate the equivalence of the two methods of solution by developing an algebraic framework for shape invariant Hamiltonians with a general change of parameters, which involves nonlinear extensions of Lie algebras.Comment: 12 pages, 2 figure