FIZIKA B 17 (2008) 3, 379 - 392
SOME RESULTS FOR A PARTICLE IN A BOX AND THEIR SUPERSYMMETRIC
SALVATORE DE VINCENZO
Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, A.P.
47145, Caracas 1041-A, Venezuela.
Received 11 October 2007; Accepted 30 July 2008
Online 17 October 2008
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.
PACS numbers: 03.65.-w, 03.65.Ge, 11.30.Pb
Keywords: particle in a one-dimensional box, SUSY QM