Uncertainity principle

Heisenberg uncertainly principle, as an expectation value. Streitwieser has eloquentiy summarized the importance of such concepts in chemical computations (42) ... 

Ventilation noise and the annoyance effects which may result have been a recurring question in recent years for researchers, occupational health services, and various aurhorities. In spite of this, there are still major shortcomings in our knowledge about the links between human effects and exposure to ventilation noise. Current regulations and recommendations are thus based on uncertain principles in certain respects. 

The quantity 4 2 represents the probability of finding the electron in the described region. It is also interpreted statistically, in the context of the Heisenberg uncertainly principle, as an expectation value. Streitwieser has eloquently summarized the importance of such concepts in chemical computations (42) ... 

A German physicist, Werner Heisenberg, formalized this idea with his uncertainly principle, which says that we cannot know the exact location or motion of an electron. Although we cannot describe the path of an electron s motion, we can speak of the probability of finding it in a given location at any time. In Figure 8.7, the darker areas represent a greater probability that the electron is present in this location. 

The Heisenberg Uncertainly Principle arises from the dual nature (wave-particle) of matter. It states that there exists an inherent uncertainty in the product of the position of a particle and its momentum, and that this uncertainty is on the order of Planck s constant. 

An important feature of operators is that they may not commute, i.e. for two particular operators A and B one may have AB — BA 0. This property has important physical consequences (see below, postulate IV and the Heisenberg uncertain principle). Because of the possible non-commutation of the operators, transformation of the classical formula (in which the commutation or non-commutation did not matter) may be non-unique. In such a case, from all the possibilities one has to choose an operator which is Hermitian. The operator A is Hermitian if, for any functions ip and < > liom its domain, one has commutalion... 

In the beginning of the twentieth century, some scientists thought that a nucleus may contain both electrons and protons. U.se the Heisenberg uncertainly principle to show that an electron cannot be confined within a nucleus. Repeat the calculation for a proton. Comment on your results. A.ssume the radius of a nucleus to... 

---