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Physics, Techniques and Procedures

Quantum theory

or quantum mechanics, theory which developed gradually over the first three decades of the 20th century and one of the major theories of modern physics. It accounts for the fact, that in the microscopic world, various physical phenomena exhibit discrete, so-called quantized states, rather than assuming a continuum of states as postulated by classical physics.

The basic tenets of quantum theory are :

1. A particle can exhibit wave-like characteristics in certain physical situations. For each particle (mass point) there exists a generally complex wave function X(x,t) (see imaginary numbers) of the spatial coordinate vector x and time t, which meets certain mathematical conditions. X(x,t) decribes the state of the particle. X(x,t) is related to the probability of finding the particle in a position x and at time t. A typical example is the following: we have to think of electron clouds around atoms rather than electron particles: we can only identify a certain probability that at any given time a given electron will be found in a certain region around the atomic nucleus; the electron cloud is thus a kind of probability distribution of finding an electron. Instead of using the position x of the particle, the momentum p of the particle can be used as that variable and is characterized by a wave function P(p,t).

2. Certain pairs of quantities, having the dimensions of energy multiplied by time, cannot be measured independently. Examples of such pairs are position and momentum, or energy and time. The product of these pairs of quantities is equal or larger than Planck's constant . As a result, in many experimental settings there remains uncertainty regarding the exact state which a system is in. This observation is called the Heisenberg uncertainty principle. The wave functions of such variable pairs, i. e. X(x,t) and P(p,t) are related by Fourier transformation FT .

3. The wave functions of quantum mechanical entities satisfy the Schroedinger equation ( Erwin Schroedinger, 1887 - 1961, Nobel laureate in physics 1933), a mathematical equation relating the energetic state of a system to its temporal evolution.

4. The states (energy, position, momentum) in which a physical system can be found, when measured, are generally quantized, i. e. only discrete values rather than a continuum of values can be measured. A typical example is the observation, that the electrons in atoms are found at certain energy levels while other energetic states are not observed (see hydrogen H ).

A corollary of these postulates is that the observed system and the observer cannot be separated but have to be considered as one system. This recognition has had far reaching consequences not only in modern physics but also in modern philosophy, replacing a dualistic world view with more holistic concepts. Quantum theory explains many physical phenomena which cannot be explained by classical physical theories. Very importantly, quantum theory is capable of fully explaining the structure of the electronic shell surrounding atoms. Quantum theoretical analysis of the structure of atoms demonstrates that there are four quantum numbers needed to unequivocally assign an electron to a state in the atomic shell (see hydrogen H ). It also explains the phenomenon that high-energy electromagnetic radiation often has a particulate rather than a wave-like character.

 

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