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The Schrodinger picture
| Content Provider | Scilit |
|---|---|
| Author | Belkić, Dževad |
| Copyright Year | 2020 |
| Description | Book Name: Principles of Quantum Scattering Theory |
| Abstract | Whenever we are talking about the problems of time evolution of physical systems, it is unavoidable to encounter the question of causality. On the level of quantum phenomena, there is no precise possibility of separating an examined physical system from a measuring instrument. This fact lends support to the assertion that the evolution of a quantum system ceases to be rigorously causal from the moment when the system is subjected to investigation. Here under the notion of measurement, we understand a selective, complex procedure of ‘preparing the conditions of the experiment and its effective performance’, with the purpose of obtaining the desired results. Stated more precisely, measurement (classical or quantal) means the following: a given apparatus, i.e. an instrument, is made to interact with the examined object in such a way that certain features of that object are reflected in the properties of the measuring device. This procedure should give certain results in the form of numbers, which are called the measured findings or experimental data. A quantum measurement is special in that it always causes a jump in the system under study to an eigenstate of the considered variable. Consequently, the result of measurement is given by an eigenvalue which corresponds to that eigenstate. Information about the $space^{1}$ will be acquired by bringing the measuring apparatus into the given $field^{2}$. Such an act is, of course, assumed not to alter the examined space. When the latter condition is not fulfilled, the problem becomes complex and one may become caught in a vicious circle. Namely, from a physical point of view, gnoseological perceptions about a field can be obtained solely via an experimental apparatus, which, however, alters the very object of the investigation. The result of such a change can, in principle, be evaluated but the importance of the phenomena by far exceeds the possibility of its quantitative assessment. The fact that, by repeating 39an experiment immediately after the first measurement and observing that the considered system is no longer in the same state, possesses an extraordinary value in itself. Such measurements are known as experiments of the second kind. As an example, we mention here measurements of the momentum of a particle by observing its collision with a certain known mass or measurements in which one would determine the polarization of a given photon flux, by observing its passage through a polaroid filter. In contrast to this, there is the usual class of experiments of the first kind, where the result in one measurement coincides with certain findings from the experiment, repeated immediately after the first $observation^{3}$. The complexity of the experiment of the second kind arises from the fact that it is no longer clear what can be attributed to the nature of the studied object and what emerges from the interaction between the apparatus and the observed system. Of course, here it would be possible to go one step further and consider an examination of the system not only through the previously mentioned notion of measurement but also the path from the human brain centres could be taken as a portion of the measuring instrument. Nevertheless, in order not to enter into the particular discipline known as the theory of measurement and to avoid altogether the area of investigations which are outside of physics, the notion of the detector will be understood as a certain intermediary object (apparatus) from the subject of the measurement to the human senses. Possible interactions between the measuring and measured objects will be neglected, so that a given quantum system, which is free from any disturbances, e.g. measurements or other perturbations, will evolve in a rigorously predictable manner. In such a case, the time-dependent Schrödinger equation: (3.1)i∂tΨ(t)= HΨ(t) ∂t≡∂/∂t |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2006-0-06687-3&isbn=9780429146497&doi=10.1201/9780429146497-7&format=pdf |
| Ending Page | 44 |
| Page Count | 7 |
| Starting Page | 38 |
| DOI | 10.1201/9780429146497-7 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2020-01-15 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Principles of Quantum Scattering Theory History and Philosophy of Science Measuring Instrument Notion of Measurement |
| Content Type | Text |
| Resource Type | Chapter |
