I noticed many PF threads mention ground state of Hydrogen atom.(adsbygoogle = window.adsbygoogle || []).push({});

At the same time it is two body problem considered to be solved by separation of variables.

It is true, of course, that we can find basis wave functions (solutions of Shroedinger equation). But why does anybody think, that ground solution is the member of this basis functions? Try find Google for theorem. You find nothing exact.

Let us take "usual ground state" wavefunction of H atom with total momentum of atom P=0

Psi (R, r) level 1, L=0 (s orbital)

Psi is the solution of Shroedinger equation where variables separated, where R is proton coordinate, and r is electron coordinate.

Consider new function:

Psi_{+}=Psi(R, r) + Psi(R-x, r-x)

where x is vector with |x| ~ 4* (atomic radius)

Every physisist who deals with double quantum dot knows, that atom levels be repelled and Psi_{+}as trial variational function, gives lower energy, than initial Psi(R, r).

Any comments?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Hydrogen atom in ground state: some puzzle

Loading...

Similar Threads - Hydrogen atom ground | Date |
---|---|

Effect of spins on hydrogen atom ground state energy | Jan 27, 2016 |

Hydrogen atom ground state wave function complex conjugate | Dec 23, 2015 |

Hydrogen atom ground state with zero orbital angular moment question. | Jan 27, 2009 |

Ground state energy of hydrogen atom | Sep 5, 2008 |

<r> of hydrogen atom in ground state | Nov 4, 2003 |

**Physics Forums - The Fusion of Science and Community**