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 partı́cula de spin 1/2 confinada por uma...

The particle in a box is simple model that has classical Hamiltonian H = p2 (using 2m 1), with limited coordinate space, -b q b, where 0 b < ∞. Using canonical quantization, this example been fully studied thanks to its simplicity, and it common for beginners understand. Despite repeated analysis, there feature puts the past results into question. In addition pointing out quantization issue, pr...

in ordinary quantum mechanics for the position uncertainty since minimum value can be tend to zero. Different theories of gravity, such as string theory, loop and black hole physics, confirm a minimal observable length. Kempf et al have formulated The length is fundamental measurement, although there no lower bound generalized principle (GUP) by modifying Heisenberg include an appearance mechan...

Pedro Alberto , Saurya Das , and Elias C. Vagenas 3‡ Departamento de F́ısica and Centro de F́ısica Computacional, Universidade de Coimbra, P-3004-516 Coimbra, Portugal Theoretical Physics Group, Dept of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, Canada T1K 3M4 and Research Center for Astronomy and Applied Mathematics, Academy of Athens, Soranou Ef...