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International Workshop on Relativistic Aspects of Nuclear Physics (RANP)

PARTICLE INTERFEROMETRY: NEW THEORETICAL RESULTS

Ulrich Heinz

Published Jan 1, 1998• 0 citations
Publisher
DOI
10.1142/9789814528917_0002

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FizB•Jan 1, 2008•1 citation
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 de-generacy of the energy eigenvalues. We also discuss the effect on the boundary conditions of requiring the invariance of the Hamiltonian under parity P ̂ and si-multaneous space and time reflection P ̂ T ̂. A condition, which depends only on the boundary values of an eigenfunction of the Hamiltonian and its derivative, deter-mines 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.