The domain of quantum mechanics

Roughly speaking quantum mechanics is required when the scale of the phenomenon being very small on the order of atomic dimensions (ten raised to the power minus ten metre). We need quantum mechanics to explain the behaviour of electrons in atoms or solids or the behaviour of atoms in molecules. We may use classical mechanics to describe the motion of macroscopic objects such as balls, Wheels, pendulums and projectiles.

An accurate establishment of domain of quantum mechanics is based directly on the Planck’s constant h = 6.626 x ten raised to the power of minus thirty four joule-sec. Planck’s constant has the dimensions of energy times time, a quantity known in classical mechanics as action. The dimensions of action can easily be shown to be the same as momentum times distance or angular momentum. Hence the following conclusion can be arrived regarding the domain of quantum mechanics.

“If the action or angular momentum involved in a given physical even is on the order of Planck’s constant, then we must use quantum mechanics to describe the event accurately. If the action or angular momentum in a physical event is orders of magnitude larger than Planck’s constant, classical mechanics will describe the event with satisfactory accuracy.”

The angular momentum of the earth orbiting around the sun is ten raised to the power one hundred and two times h, of the earth revolving about its axis is ten raised to the power sixty eight times h. The angular momentum of a bicycle wheel about its axis is ten raised to power thirty two times h, of the balance wheel in a watch approximately ten raised to the power twenty four times h. Similarly the action involved in shooting a bullet from a gun is perhaps ten raised to the power thirty five times h and that of accelerating an electron to the screen of a television tube is ten raised to the power ten times h. In all these events the quantization of the action is irrelevant because undetectably small compared with the total action involved.

Quite by contrast the angular momentum of the electron about the nucleus of an atom is only a few times h as also the angular momentum of rotation of a gaseous molecule. The action involved in the emission of radiation of an atom is generally equal to h or at most to a few times h. For these physical systems and these events the quantization of action and of angular momentum is eminently relevant and we must use quantum mechanics to calculate the properties of such systems and their interaction with applied forces.

Classical mechanics is completely definite theory in the sense that the computational procedures do not introduce any statistical uncertainties into the system themselves.

Quantum mechanics on the other hand is fundamentally a probabilistic theory.

Roughly speaking quantum mechanics is required when the scale of the phenomenon being very small on the order of atomic dimensions (ten raised to the power minus ten metre). We need quantum mechanics to explain the behaviour of electrons in atoms or solids or the behaviour of atoms in molecules. We may use classical mechanics to describe the motion of macroscopic objects such as balls, Wheels, pendulums and projectiles.

An accurate establishment of domain of quantum mechanics is based directly on the Planck’s constant h = 6.626 x ten raised to the power of minus thirty four joule-sec. Planck’s constant has the dimensions of energy times time, a quantity known in classical mechanics as action. The dimensions of action can easily be shown to be the same as momentum times distance or angular momentum. Hence the following conclusion can be arrived regarding the domain of quantum mechanics.

“If the action or angular momentum involved in a given physical even is on the order of Planck’s constant, then we must use quantum mechanics to describe the event accurately. If the action or angular momentum in a physical event is orders of magnitude larger than Planck’s constant, classical mechanics will describe the event with satisfactory accuracy.”

The angular momentum of the earth orbiting around the sun is ten raised to the power one hundred and two times h, of the earth revolving about its axis is ten raised to the power sixty eight times h. The angular momentum of a bicycle wheel about its axis is ten raised to power thirty two times h, of the balance wheel in a watch approximately ten raised to the power twenty four times h. Similarly the action involved in shooting a bullet from a gun is perhaps ten raised to the power thirty five times h and that of accelerating an electron to the screen of a television tube is ten raised to the power ten times h. In all these events the quantization of the action is irrelevant because undetectably small compared with the total action involved.

Quite by contrast the angular momentum of the electron about the nucleus of an atom is only a few times h as also the angular momentum of rotation of a gaseous molecule. The action involved in the emission of radiation of an atom is generally equal to h or at most to a few times h. For these physical systems and these events the quantization of action and of angular momentum is eminently relevant and we must use quantum mechanics to calculate the properties of such systems and their interaction with applied forces.

Classical mechanics is completely definite theory in the sense that the computational procedures do not introduce any statistical uncertainties into the system themselves.

Quantum mechanics on the other hand is fundamentally a probabilistic theory.