Quantum restriction postulate

The quantum restriction postulate Only certain quantized orbits will be allowed. These orbits are restricted to the condition where the angular momentum (I) is an integral multiple of hlljr ... 

At this point, Bohr takes a bold step and postulates the quantum restriction that the angular momentum of the electron can only take on positive integer multiple values of ft or htlTT. For an electron in a circular orbit, the angular momentum is m ru, so... 

The Sommerfeld model for Ne is shown in figure 2.8. The He atom presented a special problem as the quantum numbers restrict the two electrons to the same circular orbit, on a collision course. One way to overcome this dilemma was by assuming an azimuthal quantum number k = for each electron, confining them to coplanar elliptic orbits with a common focal point. To avoid interference they need to stay precisely out of phase. This postulate, which antedates the discovery of electron spin was never seen as an acceptable solution to the problem which eventually led to the demise of the Sommerfeld model. 

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. 

Returning now to a discussion of the Redfield equations (40) we first note that, with our choice in (39), the only nondiagonal elements that are coupled to each other are p,2 and P34. Except for the driving-field terms these equations therefore have a form very similar to the modified Bloch equations postulated by McConnell. The quantum-mechanical derivation of (40), however, leads to new insight and restrictions in the use of these equations in the optical domain (Section IV). 

The assumptions on which quantum mechanics is based may be given in the form of postulates I-VI, which are described next. For simplicity, we will restrict ourselves to a single particle moving along a single coordinate axis x (the mathematical foundations of quantum mechanics are given in Appendix B available at booksite.elsevier.com/978-0-444-59436-5 on p. el). 

In 1913, Bohr proposed a model for the hydrogen atom that appeared to explain the line spectra discussed in Section 6.2. The motion of the electron around the nucleus was considered to be similar to the motion of a planet around the sun, the gravitational attraction that keeps the planet in a circular or an elliptical orbit being replaced by the coulom-bic attraction between the electron and the positively charged nucleus. To account for the line spectra, Bohr postulated that the angular momentum of the electron was restricted to multiple values of fl. This was an arbitrary postulate at the time it was made, but it comes naturally from the quantum mechanical description of a particle moving in a circle, as we have already seen in Section 5.1.3. 

The assumptions on which quantum mechanics is based are given by the following postulates I-VI. For simplicity, we will restrict ourselves to a single particle... 

Equation 10.10 is known as the Schrodinger equation and is a very important equation in quantum mechanics. Although we have placed certain restrictions on wavefunctions (continuous, single-valued, and so on), up to now there has been no requirement that an acceptable wavefunction satisfy any particular eigenvalue equation. However, if P is a stationary state (that is, if its probability distribution does not depend on time), it must also satisfy the Schrodinger equation. Also note that equation 10.10 does not include the variable for time. Because of this, equation 10.10 is more specifically referred to as the time-independent Schrodinger equation. (The time-dependent Schrodinger equation will be discussed near the end of the chapter and represents another postulate of quantum mechanics.)... 

Light emitted from excited atoms and ions consists of a limited number of wavelength components, which can be dispersed by a prism to produce atomic or line spectra (Fig. 8-11). The first attempt to explain atomic (line) spectra was made by Niels Bohr who postulated that the electron in a hydrogen atom exists in a circular orbit designated by a quantum number, n, that restricts the energy of the electron to certain values (equation 8.5). 

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