New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
نویسنده
چکیده
New types of irreducible second order Darboux transformations for the one dimensional Schrödinger equation are described. The main feature of such transformations is that the transformation functions have the eigenvalues grater then the ground state energy of the initial (or reference) Hamiltonian. When such a transformation is presented as a chain of two first order transformations, an intermediate potential is singular and therefore intermediate Hamiltonian can not be Hermitian while the final potential is regular and the final Hamiltonian is Hermitian. Second derivative supersymmetric quantum mechanical model based on a transformation of this kind exhibits properties inherent to models with exact and broken supersymmetry at once. PACS: 03.65.Ge; 03.65.Fd; 03.65.Ca
منابع مشابه
Factorization of nonlinear supersymmetry in one-dimensional Quantum Mechanics. I: general classification of reducibility and analysis of the third-order algebra
We study possible factorizations of supersymmetric (SUSY) transformations in the one-dimensional quantum mechanics into chains of elementary Darboux transformations with nonsingular coefficients. A classification of irreducible (almost) isospectral transformations and of related SUSY algebras is presented. The detailed analysis of SUSY algebras and isospectral operators is performed for the thi...
متن کاملPolynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
2 We give the classification of second-order polynomial SUSY Quantum Mechanics in one and two dimensions. The particular attention is paid to the irreducible supercharges which cannot be built by repetition of ordinary Darboux transformations. In two dimensions it is found that the binomial superalgebra leads to the dynamic symmetry generated by a central charge operator.
متن کاملSupersymmetric Construction of three-dimensional isospectral systems
The concept of supersymmetry arose in the study of elementary particle physics. The term “supersymmetry” was originally used in reference to the symmetry of bosons and fermions, which behave according to different statistical laws. Supersymmetry is widely regarded as a necessary concept for unifying all the elementary forces. The concept of supersymmetry was originally formulated in the framewo...
متن کاملFactorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility
In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients. We define the class of potentials that are invariant under the Darboux – Crum transformations and prove a number of lemmas and theorems substantiating the formulated formerly conjectures o...
متن کاملTime-dependent Parasupersymmetry in Quantum Mechanics
Parasupersymmetry of the one-dimensional time-dependent Schrödinger equation is established. It is intimately connected with a chain of the time-dependent Darboux transformations. As an example a parasupersymmetric model of nonrelativistic free particle with threefold degenerate discrete spectrum of an integral of motion is constructed. 1. Supersymmetric quantum mechanics originally introduced ...
متن کامل