Limit-point / limit-circle classification of second-order differential operators arising in PT quantum mechanics

Limit-point/limit-circle Results for Forced Second Order Differential Equations

In this paper, the authors consider both the forced and unforced versions of a second order nonlinear differential equation with a p-Laplacian. They give sufficient conditions as well as necessary and sufficient conditions for the unforced equation to be of the strong nonlinear limit-circle type, and they give sufficient conditions for the forced equation to be of the strong nonlinear limit-cir...

Limit Circle/Limit Point Criteria for Second-Order Sublinear Differential Equations with Damping Term

and Applied Analysis 3 2. Main Results To simplify notations, let α 1/2 k 1 and β 2k 1 /2 k 1 . We define

Limit Circle/Limit Point Criteria for Second-Order Superlinear Differential Equations with a Damping Term

Limit - Point / Limit - Circle Results for Equations with Damping

and Applied Analysis 3 and let constant δ be given by

Classical Limit of Quantum Mechanics

para o valor esperado de uma dada observável fı́sica A = A(p, q, t) representada pelo operador Â. As equações (1) e (2) são válidas desde que o potencial externo V varie vagarosamente dentro de um pacote de onda bem localizadoψPE (Pacote de Ehrenfest). Assim, de acordo com os livros-texto [1], as equações de Newton são obtidas como limite clássico da equação de Schrödinger. No entanto, Ballentin...