Quantum Mechanics & F=ma: What Replaces F=ma in Atoms?

[Cheman]

I have read the equation F = ma "does not apply directly on the very small scale of the atom where quantum mechanics must be used." What exactly is therefore used instead of F= ma?

Furthermore, would it be possible (if we ignore the complexity of them) to use these quantum calculations to work out macro effect? eg - the acceleration a 1kg mass would udergo if pushed by a 45N force? Does this therefore mean that the quantum calculation is the more "correct" way and that F=ma just happens also to work for things on a large scale?

Thanks in advance.

 

[dextercioby]

I have read the equation F = ma "does not apply directly on the very small scale of the atom where quantum mechanics must be used." What exactly is therefore used instead of F= ma?

1.The assertion inserted is correct.
2.We use Schroedinger's equation $$\frac{\partial|\Psi>}{\partial t}=<br /> \frac{1}{i\hbar}\hat{H}|\Psi>$$.It describes the dynamics of the system,i.e.the time evolution of the state vector $|\Psi>$.

Furthermore, would it be possible (if we ignore the complexity of them) to use these quantum calculations to work out macro effect? eg - the acceleration a 1kg mass would udergo if pushed by a 45N force? Does this therefore mean that the quantum calculation is the more "correct" way and that F=ma just happens also to work for things on a large scale?

The answer to your first 2 questions is "NO".No,each theory has its range of application.Quantum mechanics is just the natural extent of classical mechanics (it bears the name "Mechanics",right??)in Hamiltonian formulation to atom size (generically said,it could be nucleons->molecules) interactions."F=ma" works at macroscopical scale because experiment allows it.At macroscopical scale there isn' any room for "theory",or "theoretical physics".Everything,every mathematical relation must be experimentally confirmed,as for the quantum theory,well,it would be utopic to say that every mathematical abstraction must be verified experimentally,as it is the case for classical macroscopical theories.

Thanks in advance.

"Thank me when it's over"

 

[seratend]

"F=ma" works at macroscopical scale because experiment allows it.At macroscopical scale there isn' any room for "theory",or "theoretical physics".

This is a very personal point of view quite analog to the Inquisition assertions. I do not think that everyone subscribes to it. GR theorists should be disappointed by such an assertion (poor Einstein ).


Seratend.

 

[dextercioby]

This is a very personal point of view quite analog to the Inquisition assertions. I do not think that everyone subscribes to it. GR theorists should be disappointed by such an assertion (poor Einstein ).


Seratend.

I think u knew pretty clear i wasn' referring to GR.GR is a "classical" theory wrt to quantum physics,but it' a branch of theoretical physics at a macroscopical level.Had i included GR in my assertion,it ment we,at a conceptual level,could measure abstract things like the scalar curvature of a space-time caused by Earth or any other celestial body.Or why not,the whole 20 independent components of the Riemann tensor.Or show by experiment that,out of 256 possible components,u can express 236 wrt to only 20.Those things are impossible.
Frankly,u were right.At macroscopical level,there's room ony for GR out of the theoretical physical side of nature.I shouldn't have made a generalization,but i hoped people would understand it would have been ludierous of me to include GR.

Daniel.

 

[Cheman]

Is there a way to possibly connect the classical methods of dealing with forces (ie - F=ma) and quantum ways? After all they are dealing with the same things - those being forces and resulting motion.

 

[seratend]

Is there a way to possibly connect the classical methods of dealing with forces (ie - F=ma) and quantum ways? After all they are dealing with the same things - those being forces and resulting motion.

You have the de Brooglie-Bohm reformulation of QM with the introduction of a quantum potential in the equation that depends on the QM statistics (Hamilton-jacobi approach).
You also have analog direct F=ma equations using langevin type forces (model somewhat analog to the brownian motion), e.g. Nelson, Phys. rev. 1966 "derivation of the SE from Newtonian mechanics".
However, If you remove the interpretation problem, you almost always get a formal equivalent model that is more difficult to solve than the classical QM equations.

Seratend.

 

[somy]

Well it is in fact impossible to define acceleration to a quantum mechanic scale, system! where we just talk about the probability of finding a particle somewhere.
I think you should be familiar with Heisenberg's uncetainty principle. It is an example of some experiment that shows our macroscopic view of dynamics can not be applied to for example "an electron".
So the scientist developed a statistical based theory that discusses about the dynamics of such systems. There we just deal with the probability of existing.
Of course we always try to find some similarities between the classical and quantum mechanics, in order to make the shape of theories uniqe.

 

[Galileo]

Furthermore, would it be possible (if we ignore the complexity of them) to use these quantum calculations to work out macro effect? eg - the acceleration a 1kg mass would udergo if pushed by a 45N force? Does this therefore mean that the quantum calculation is the more "correct" way and that F=ma just happens also to work for things on a large scale?

There is the old Ehrenfest's Theorem.

$$\frac{d}{dt} \langle x \rangle = \frac{1}{m}\langle p \rangle$$

$$\frac{d}{dt}\langle p \rangle = \langle -\frac{\partial V}{\partial x}\rangle$$

So when the spreading of the wavefunction can be ignored we may take the 'position' of the particle to be the expectation value of its position.
We then recover Newtons 2nd Law.