Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model
In this paper, a finite memory, non-causal Volterra model is proposed to estimate the potential functions in various inverse quantum mechanical problems, where the bound or scattered wave functions are used as inputs of the Volterra system, while the potential is the desired output. Two simple examp...
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| Format: | Article |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/8/1257 |
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| author | Gábor Balassa |
| author_facet | Gábor Balassa |
| author_sort | Gábor Balassa |
| collection | DOAJ |
| description | In this paper, a finite memory, non-causal Volterra model is proposed to estimate the potential functions in various inverse quantum mechanical problems, where the bound or scattered wave functions are used as inputs of the Volterra system, while the potential is the desired output. Two simple examples are given to show the model capabilities, where in both cases, a really good match is achieved for a very wide range of potential functions. The first example is a simple one-dimensional bound state problem, where the wave function of the first bound state is used as input to determine the model potential. The second example is a one-dimensional scattering problem, where the scattered wave is used as the system input. In both cases, a higher order, non-causal description is needed to be able to give a good estimation to the solution of the inverse problem. The model sensitivity to input perturbations is also examined, showing that the Volterra representation is capable of giving a robust estimate to the underlying dynamical system. The model could be useful in real-life situations, where the scattering potential should be found from measured data, where the precise equations that govern the dynamics of the system are not known. |
| first_indexed | 2024-03-09T10:31:49Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:31:49Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-2b9574e3e23c47fd9830aa714e0ea3542023-12-01T21:12:04ZengMDPI AGMathematics2227-73902022-04-01108125710.3390/math10081257Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra ModelGábor Balassa0Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, H-1525 Budapest, HungaryIn this paper, a finite memory, non-causal Volterra model is proposed to estimate the potential functions in various inverse quantum mechanical problems, where the bound or scattered wave functions are used as inputs of the Volterra system, while the potential is the desired output. Two simple examples are given to show the model capabilities, where in both cases, a really good match is achieved for a very wide range of potential functions. The first example is a simple one-dimensional bound state problem, where the wave function of the first bound state is used as input to determine the model potential. The second example is a one-dimensional scattering problem, where the scattered wave is used as the system input. In both cases, a higher order, non-causal description is needed to be able to give a good estimation to the solution of the inverse problem. The model sensitivity to input perturbations is also examined, showing that the Volterra representation is capable of giving a robust estimate to the underlying dynamical system. The model could be useful in real-life situations, where the scattering potential should be found from measured data, where the precise equations that govern the dynamics of the system are not known.https://www.mdpi.com/2227-7390/10/8/1257inverse scatteringVolterra modelnonlinear systems |
| spellingShingle | Gábor Balassa Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model Mathematics inverse scattering Volterra model nonlinear systems |
| title | Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model |
| title_full | Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model |
| title_fullStr | Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model |
| title_full_unstemmed | Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model |
| title_short | Estimating Scattering Potentials in Inverse Problems with a Non-Causal Volterra Model |
| title_sort | estimating scattering potentials in inverse problems with a non causal volterra model |
| topic | inverse scattering Volterra model nonlinear systems |
| url | https://www.mdpi.com/2227-7390/10/8/1257 |
| work_keys_str_mv | AT gaborbalassa estimatingscatteringpotentialsininverseproblemswithanoncausalvolterramodel |