Supersymmetric Dynamical Invariants

Details Supersymmetric Dynamical Invariants Supersymmetric Dynamical Invariants

2001-04-13

arxiv.org/abs/quant-ph/0104071v1

J.Phys. A34 (2001) 4493-4506

Physics

Quantum Physics

Plain Latex, accepted for publication in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/34/21/306

We address the problem of identifying the (nonstationary) quantum systems that admit supersymmetric dynamical invariants. In particular, we give a general expression for the bosonic and fermionic partner Hamiltonians. Due to the supersymmetric nature of the dynamical invariant the solutions of the time-dependent Schr\"odinger equation for the partner Hamiltonians can be easily mapped to one another. We use this observation to obtain a class of exactly solvable time-dependent Schr\"odinger equations. As applications of our method, we construct classes of exactly solvable time-dependent generalized harmonic oscillators and spin Hamiltonians.

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