Original scientific paper
Some results for a particle in a box and their supersymmetric partners
Salvatore De Vincenzo
; Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, A.P. 47145, Caracas 1041-A, Venezuela
Abstract
Some physical restrictions and their influences on the boundary conditions for a particle in a one-dimensional box are pointed out. We discuss the invariance of the corresponding Hamiltonian under time-reversal [^T] and its relation with the degeneracy of the energy eigenvalues. We also discuss the effect on the boundary conditions of requiring the invariance of the Hamiltonian under parity [^P] and simultaneous space and time reflection [^P][^T]. A condition, which depends only on the boundary values of an eigenfunction of the Hamiltonian and its derivative, determines if the corresponding eigenvalue satisfies the inequality E > V(x)=const, V(x) being the potential inside the box. Once these results have been presented, we choose various representative analytically solvable examples of boundary conditions (Hamiltonians) and supersymmetrize the corresponding problems. We find real and complex valued supersymmetric partner potentials among all these systems.
Keywords
particle in a one-dimensional box; SUSY QM
Hrčak ID:
304905
URI
Publication date:
1.9.2008.
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