Quantum Hamiltonians from level statistics via dressing transformations. (English) Zbl 0811.65053
Summary: We use the dressing transformation in order to reconstruct one- dimensional Hamiltonians starting from their spectra. Whenever the given spectrum departs from oscillator-like local behaviour the resulting potential is fractal. An estimate of this fractal dimension is presented.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 37-XX | Dynamical systems and ergodic theory |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
Keywords:
reconstruction from spectra; Schrödinger equation; oscillation; quantum chaos; autonomous Hamiltonian systems; dressing transformation; fractal dimensionReferences:
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