Controlling Electron Orbitals: The Key to Creating a Hydrogen Atom?

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Creating a hydrogen atom involves understanding the mechanics of electron and proton interactions, where the electron's speed and direction relative to the proton dictate whether it will orbit. Classical mechanics describes this with a 1/r^2 potential well, leading to elliptical or parabolic orbits, while quantum mechanics introduces wave-functions that complicate the concept of orbits. The distinction between classical and quantum perspectives is significant, as the latter involves solutions to the Schrödinger equation in a Coulomb potential. Additionally, radiation effects must be considered, as they can lead to the decay of orbits. Ultimately, a deeper understanding of quantum mechanics is necessary to fully grasp the nature of atomic formation.
cragar
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how do i make a hydrogen atom , if i shoot an electron by a proton will it start to orbit the proton , what dictates whether it will orbit or not .
 
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It is primarily a question of mechanics - similar to a planet in relation to a star. Basically it depends on the speed and direction of the electron relative to the proton.
 
Does it have anything to do with their wave-functions overlapping .
 
The classical and quantum-mechanical answers to this question are totally different.

Classically you have the standard 1/r^2 potential well and can solve the two-body problem analytically to find the conditions for capture and escape (which turn out to be elliptical and parabolic orbits), given a known starting position and velocity. However, whether you count an electron orbiting a proton with an eccentricity of 0.99 as an "atom" might depend on whether you call Pluto a planet! You also need to disregard radiation which will lead to fast decaying orbits.

Quantum mechanically I know a lot less about. You can probably find solutions to the static Schroedinger equation in a coulomb potential and argue they represent an atom, but a free electron appears in the maths as a wave with a time-dependant element so I don't know how it would be approached.
 
I see thanks for your answers maybe i will wait until i take QM
 

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