Relativistic particle in a box

Abstract

The problem of a relativistic spin 1/2 particle confined to a one-dimensional box is solved in a way that resembles closely the solution of the well known quantum-mechanical textbook problem of a non-relativistic particle in a box. The energy levels and probability density are computed and compared with the non-relativistic case. Resumo. O problema de uma partícula de spin 1/2 confinada por uma caixa a uma dimensãoé resolvido de uma maneira muito semelhanteà da resolução do problema de uma partícula no-relativista numa caixa referido em muitos livros introdutórios de Mecânica Quntâica. Os níveis de energia e a densidade de probabilidade são calculados e comparados com os valores não-relativistas.

On the relativistic L - S coupling

“…In the present paper we use the same procedures as in [2] to provide a bridge between known relativistic and nonrelativistic solutions in the 3-dimensional spherical case, with special emphasis on the L − S coupling. Berry and Mondragon [3] have also applied similar methods in the framework of the Dirac equation in two spatial dimensions.…”

Pair states in one-dimensional Dirac systems

“…The spinor components of the eigenfunctions of a square well need not necessarily be continuous at the well's edge [54] since they are solutions to a system of first-order differential equations containing a potential that is itself discontinuous. By analyzing the behavior of the wave function for our smooth potential, in the limit in which it approaches a smooth square well, one can obtain the appropriate boundary conditions for the spinor components of the true square well at the well's edge.…”

Generalized relativistic wave equations with intrinsic maximum momentum

“…This can be viewed as the position dependent rest mass term, i.e. the MIT bag model in quark confinement to avoid Klein paradox [3]. The potentials are assumed to be linear and take the form of…”

“…It was well studied that when the linear potential is introduced as a Lorentz scalar in the relativistic wave equation (RWE) such as Klein-Gordon (KG) or Dirac equation, quantum confinement is possible [1,2]. This is because a scalar potential in RWE is equivalent to a position dependent of the rest mass similar to the MIT bag model of quark confinement [3].…”