Free electron path without a nearby proton

[Tareq Naushad]

TL;DR Summary

Quantum properties of an free electron outside atom

In absence of a positive electric field created by proton what type of behavior an electron shows? I am talking about a free electron like from a electron gun in deep space . Pauli's exclusion, orbitals, energy level etc. which are normal in an atom for electron will be absent for an electron out from an atom. So what type of quantum behavior it shows then ?

 

[Dale]

It still has quantized spin and charge.

 

[Tareq Naushad]

thanks. what about its allowable energy level, uncertainty of position, momentum etc. because now it is not governed by the field of +ve proton

 

[Nugatory]

what about its allowable energy level, uncertainty of position, momentum etc. because now it is not governed by the field of +ve proton

We're still solving Schrodinger's equation to find the wave function. Schrodinger's equation includes a term for the potential, which will be the Coulomb potential for an electron near a proton (whether bound or not) and zero for an isolated (and therefore obviously unbound) electron in vacuum.

The bound states will have discrete eigenvalues. The unbound ones will have a continuous spectrum (although there are some mathematical complications here that we can ignore for now) quantum mechanics still works: position/momentum uncertainty still works, Schrodinger's equation governs the evolution of the wave function, we can even in principle do a double-slit experiment with a beam of free electrons and produce an interference pattern.