Quantization of angular momentum

The B cyclic theorem is a Lorentz invariant construct in the vacuum and is a relation between angular momentum generators [42], As such, it can be used as the starting point for a new type of quantization of electromagnetic radiation, based on quantization of angular momentum operators. This method shares none of the drawbacks of canonical quantization [46], and gives photon creation and annihilation operators self-consistently. It is seen from the B cyclic theorem ... 

Figure 6.5 Space quantization of angular momentum, showing the case 1 = 1.

For further progress, we need some restriction on the possible values of r or u. This is where we can introduce the quantization of angular momentum L = r x p. Since p is pcipendicular to r, we can write simply... 

The existence of discrete orbits and quantized energies follows directly as a consequence of the quantization of angular momentum. 

The energies of macroscopic objects, as well as those of microscopic objects, are quantized, but the effects of the quantization are not seen because the difference in energy between adjacent states is so small. Apply Bohr s quantization of angular momentum to the revolution of Earth (mass 6.0 X 10 " kg), which moves with a velocity of 3.0 X 10" m s in a circular orbit (radius 1.5 X 10 m) about the sun. The sun can be treated as fixed. Calculate the value of the quantum number n for the present state of the Earth-sun system. What would be the effect of an increase in by 1 ... 

Balmer s formula, but- also to establish one of the most important results of quantum mechanics the quantization of angular momentum in units of A/2tt. This result arises from the analysis in his paper it is not his starting point. Bohr s quantum postulate was based on Planck s assumption of the quantization of the energy of harmonic oscillators. By analogy with this, and arguing from a correspondence with classical physics, he set a restrictive condition on the mechanically possible electron orbits, and postulated that this limited set of orbits should be non-radiating. 

The quantization of angular momentum is nhl2n, where n is the principal quantum number. As the principal quantum number increases... 

Here we restrict ourselves to the case 5 W and to the states with m = n—1, i.e. the states with meiximal possible values of the magnetic quantum number m. Parameters of the classiced electron orbit are determined from equilibrium conditions analogous to the quantization of angular momentum ... 

As many authors note, the quantization of angular momentum assumed by Bohr as weU as the notion that electrons in stationary states do not radiate was somewhat ad hoc and only justified later by Erwin Schrodinger s approach to calculating the energy of the hydrogen atom. 

The above results for the quantization of angular momentum have been derived for a single particle, but the same results hold for two masses (say, a diatomic molecule) rotating around their center of mass, when / is the moment of inertia of the system. This opens the way to the quantum mechanical treatment of rotating molecules. 

Equation 3.21 is used to calculate the rotational partition function. Each rotational energy level is 2Z+1 times degenerate because of the vectorial quantization of angular momentum, so it must be counted as many times in the summation. On the other hand, whenever the molecular symmetry is such that identical atoms exchange their positions because of a molecular rotation, the summation must be divided by an appropriate symmetry number, a [2]. Then ... 

Because of the quantization of angular momentum, simple rules exist for the vector sum of two angular momenta. If one source has the quantum number and the other source /2, the possible values of / for the composite system range in steps of 1 from i + Jz to /i - /21 ... 

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