Hard confinement of a two-particle quantum system using the variational method
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916456415887360 |
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| author | sabbah, Nataly Rafat Al-Masaeed, Mohamed Ghaleb Al-Jamel, Ahmed |
| author_facet | sabbah, Nataly Rafat Al-Masaeed, Mohamed Ghaleb Al-Jamel, Ahmed |
| contents | The variational method is used to study the hard confinement of a two-particle quantum system in two potential models, the Cornell potential and the global potential, with Dirichlet-type boundary conditions at various cut-off radii. The trial wavefunction is constructed as the product of the $1S$ free hydrogen atom wavefunction or $1S$ free harmonic oscillator wavefunction times a cut-off function of the form $(r-z)$ to ensure hard entrapment within a sphere of radius $z$. The behavior of $|ψ|^2$, the wavefunction at the origin (WFO), and the mean radius $\ev{r}$ are computed for different situations and compared for the two potential models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10788 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hard confinement of a two-particle quantum system using the variational method sabbah, Nataly Rafat Al-Masaeed, Mohamed Ghaleb Al-Jamel, Ahmed Quantum Physics The variational method is used to study the hard confinement of a two-particle quantum system in two potential models, the Cornell potential and the global potential, with Dirichlet-type boundary conditions at various cut-off radii. The trial wavefunction is constructed as the product of the $1S$ free hydrogen atom wavefunction or $1S$ free harmonic oscillator wavefunction times a cut-off function of the form $(r-z)$ to ensure hard entrapment within a sphere of radius $z$. The behavior of $|ψ|^2$, the wavefunction at the origin (WFO), and the mean radius $\ev{r}$ are computed for different situations and compared for the two potential models. |
| title | Hard confinement of a two-particle quantum system using the variational method |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.10788 |