Like the pauli expulsion principle and the heisenberg uncertainty principle which stand true for plank space (quantum mechanics), can they be influenced by the thought of classical mechanics? Like classical mechanics clearly able to predict the position and momentum of electron at given time t while quantum mechanics fails. So I question that kindly see the below paper as lay man work to relate classical and quantum mechanics .
Article Electrons Dynamics in Semi-Conductor: Various Laws Governing...
Before proposing something is it better to know the existing knowledge?
Dear Shaikh,
You shared this question with me. Thank you for that. Your question is a very basic question and the scientists of the atomic physics answered it around the 20s and 30s of the last century. Here, i will outline their answer out of my experience and under standing.
The observations showed and still show that the classical Newtonian mechanics gives correct results when applied to describe the motion of macroscopic bodies in potential field. On the other side, When Newtonian mechanics was used at that time to describe the motion of the electrons in a confined and limited potential field such as the motion of electrons in atoms, it gave results which are far from the experimental observations.
The experimental observations resulting from the the interaction between photons of light and the atoms pointed out that the electrons in the atoms have quarantined energy , momentum, and orbits. This stands in a basic contradiction with the observation of the classical mechanics where the energy, the momentum and position are continuous.
The scientists came to the conclusion that the motion of the confined microscopic particles such as the motion of electrons in atoms and molecules are governed by other laws of motion other than the classical mechanics
Three great scientists founded the principles of a new mechanics called it the quantum mechanics that when applied to solve for the motion of electrons and microscopic bodies gives results in agreement with the experimental observations.
It has been proved that the quantum mechanics is of more general applicability than the classical mechanics.
The classical mechanics is applicable for the motion of macroscopic bodies and unconfined motion of microscopic bodies while quantum mechanics is applicable for all bodies in confined and unconfined spaces.
In order to obtain quantization naturally, one has to assume that the masses move as waves.
Accordingly,Heisenberg formulated his well known uncertainty principle. De Broglie expressed his postulate of assigning periodicity to the electron motion Lambda=h/p, with p the momentum of the moving mass. Schroedinger then formulated the basic law of the wave motion of the particles.His equation is analog to the second law of Newton in the classical mechanics.
Now let us ask the question when do we use quantum mechanics to describe the motion of a mass in a potential field?
The answer is given by De BROGLIE posulate:
Lambda= Plancks constant/ the momentum of the mass
If lambda is in the order of the particle size and or the space in which it moves the observed motion will be wavemechanical one.
On the other side. if the wavelength is much smaller than the size of the body and or the space in which it moves the observed motion will be Newtonian.
Examples:
-Electrons moving in vacuum tube were described successfully using classical mechanics.
-The motion of Free electrons in solids also is successfully described using classical mechanics. Provided that the quantummechanical effects are taken int consideration using the effective mass concept.
-Bound electrons also termed confined in the space must be treated quantum mechanically. and
-The motion of all macroscopic bodies is solved using classical mechanics.
At last, i hope that i shad some light on the applicability of the classical mechanics and wave mechanics.
I am sorry. It is a long comment.
Thank you
In a fluctuating environment the answer is certainly yes. see the attached paper.
@piero thanx for the link
@abdelhalim sir thanks for revising me the concept of both and applicability area, it really helped
but sir my basic thing i am stressing on is this " suppose in a plank space where every electrons have quantized distinct energy level which is in understanding with practical results, but sir the issue have arised by some querry that what is the probablity of two electrons which are at closely spaced distinct energy levels of not colliding with each other, given the fact that these are assumed to be waves with random motion. Because if they have even minute probablity of colliding then at that point their position and momentum both will be predictable"
Dear Ingo, you may try this: I. Bialyniki-Birula, M., Cieplak, J., Kaminski, “Theory of Quanta”, Oxford University press, Ny, (1992)I.
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