How Are Quantum Eigenfunctions of Hydrogen Atom Related To Its Classical Elliptic Orbits?
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917482210525184 |
|---|---|
| author | Yin, Yixuan Wang, Tiantian Wu, Biao |
| author_facet | Yin, Yixuan Wang, Tiantian Wu, Biao |
| contents | We show that a highly-excited energy eigenfunction $ψ_{nlm}(\vec{r})$ of hydrogen atom can be approximated as an equal-weight superposition of classical elliptic orbits with energy $E_n$ and angular momentum $L=\sqrt{l(l+1)}\hbar$, and $z$ component of angular momentum $L_z=m\hbar$. This correspondence is established by comparing the quantum probability distribution $|ψ_{nlm}(\vec{r})|^2$ and the classical probability distribution $p_c(\vec{r})$ of an ensemble of such orbits. This finding illustrates a general principle: in the semi-classical limit, an energy eigenstate of a quantum system is in general reduced to a collection of classical orbits, rather than a single classical orbit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How Are Quantum Eigenfunctions of Hydrogen Atom Related To Its Classical Elliptic Orbits? Yin, Yixuan Wang, Tiantian Wu, Biao Quantum Physics Atomic Physics We show that a highly-excited energy eigenfunction $ψ_{nlm}(\vec{r})$ of hydrogen atom can be approximated as an equal-weight superposition of classical elliptic orbits with energy $E_n$ and angular momentum $L=\sqrt{l(l+1)}\hbar$, and $z$ component of angular momentum $L_z=m\hbar$. This correspondence is established by comparing the quantum probability distribution $|ψ_{nlm}(\vec{r})|^2$ and the classical probability distribution $p_c(\vec{r})$ of an ensemble of such orbits. This finding illustrates a general principle: in the semi-classical limit, an energy eigenstate of a quantum system is in general reduced to a collection of classical orbits, rather than a single classical orbit. |
| title | How Are Quantum Eigenfunctions of Hydrogen Atom Related To Its Classical Elliptic Orbits? |
| topic | Quantum Physics Atomic Physics |
| url | https://arxiv.org/abs/2411.18890 |