# Nonlinear supersymmetry for spectral design in quantum mechanics

@article{Andrianov2004NonlinearSF, title={Nonlinear supersymmetry for spectral design in quantum mechanics}, author={A. A. Andrianov and U. F.CannataSankt-PetersburgState and Infn and Bologna}, journal={Journal of Physics A}, year={2004}, volume={37}, pages={10297-10321} }

A nonlinear (polynomial, N-fold) SUSY approach to preparation of quantum systems with pre-planned spectral properties is reviewed. The full classification of ladder-reducible and irreducible chains of SUSY algebras in one-dimensional QM is given. Possible extensions of SUSY in one dimension are described. They include (no more than) N = 2 extended SUSY with two nilpotent SUSY charges which generate the hidden symmetry acting as a central charge. Embedding stationary quantum systems into a non…

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## References

SHOWING 1-10 OF 242 REFERENCES

### Nonlinear supersymmetry in quantum mechanics: Algebraic properties and differential representation

- Mathematics, Physics
- 2003

### Higher Order SUSY in Quantum Mechanics and Integrability of Two-dimensional Hamiltonians

- Mathematics, Physics
- 1996

The new method based on the SUSY algebra with supercharges of higher order in derivatives is proposed to search for dynamical symmetry operators in 2-dim quantum and classical systems. These symmetry…

### Matrix Hamiltonians: SUSY approach to hidden symmetries

- Physics
- 1997

A new supersymmetric approach to dynamical symmetries for matrix quantum systems is explored. In contrast to standard one-dimensional quantum mechanics where there is no role for an additional…

### Polynomial supersymmetry and dynamical symmetries in quantum mechanics

- Physics, Mathematics
- 1995

A polynomial generalization of supersymmetry in quantum mechanics in one and two dimensions is proposed. Polynomial superalgebras in one dimension are classified. In two dimensions, a detailed…

### A SUSY approach for investigation of two-dimensional quantum mechanical systems*

- Physics
- 2004

Different ways to incorporate two-dimensional systems which are not amenable to separation of variables treatment into the framework of supersymmetrical quantum mechanics (SUSY QM) are analysed. In…

### CLASSICAL INTEGRABLE TWO-DIMENSIONAL MODELS INSPIRED BY SUSY QUANTUM MECHANICS

- Mathematics, Physics
- 1998

A class of integrable two-dimensional (2D) classical systems with integrals of motion of fourth order in momenta is obtained from the quantum analogues with the help of deformed SUSY algebra. With…

### Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states

- Mathematics
- 1999

Using an iterative construction of the first-order intertwining technique, we find k-parametric families of exactly solvable anharmonic oscillators whose spectra consist of a part isospectral to the…

### Polynomial SUSY in quantum mechanics and second derivative Darboux transformations

- Mathematics, Physics
- 1994