Space quantization of electron orbits ?

[mkbh_10]

The values of theta that represent the angle b/w orbital quantum no. (l) & magnetic field direction can never by pi or 0 deg as then the magnetic quantum no . will have non integral values & and also the direction of orbital quantum no . & magnetic field will be parallel which means the electron will have circular orbit which is not possible as a particle under the action of a central force field has elliptical orbit . No cone around the magnetic field will be traced out . Is my reasoning correct ??

 

[mkbh_10]

Will sum1 ans this ??

 

[jambaugh]

Some issues:
Circles are ellipses so I don't understand your argument on that point.

You're talking quantum theory so "elliptical orbits" is also meaningless in this context. The quantum description precludes constantly knowing the exact position over time and saying this follows any specific orbit. [Else you'd also know the momentum or you'd have to make the mass variable and you'd no longer have an "electron".]

You're talking quantum mechanics so it is improper to speak of "the direction of the orbital quantum number $$\ell$$" as if it is an observable. You pick a direction to measure and in that direction you measure a component $$\ell$$. There is no reason you can't (in principle) decide to measure the component in line with a specific magnetic field. (As a practical matter you usually use magnetic fields to measure this so this is problematic.)

Due to the non-commutativity of distinct components of orbital (or spin) angular momentum you cannot say anything about the other two components once you measure one.

I think what you're getting at is the fact that if you treat the total orbital angular momentum as if it were coming from an orbiting point mass then the component measured in the direct of the magnetic field (or any other one direction) will always be insufficient to account for the total (root sum of square of components). One then reasons that there is some component in the other two cardinal directions contributing to this total. That's OK except that it is improper to speak assuredly about that which fundamentally cannot be observed...most especially in quantum theory.

It's not just that classical point objects have quantized states. They don't have states as such at all but only potential observables not all of which can be made empirically meaningful at the same time.