Quantum mechanics as applied mathematical statistics

Quantum Mechanics and Statistical Description of Results of Measurement

“…In this section, we investigate the mean value of the product of the coordinate and momentum which is important in the uncertainty relations (see also (Skála,Čížek & Kapsa, 2011)). …”

“…(Cover & Thomas, 1991;Fisher, 1925)). In our case, it can be introduced in the following simple way (see also (Frieden, 1998;2004;Frieden & Soffer, 1995;Kapsa et al, 2010;Reginatto, 1998;Skála & Kapsa, 2005a;2007a;Skála,Čížek & Kapsa, 2011)). For various applications of the Fisher information in physics and chemistry see e.g.…”

“…(1) and our discussion in the preceding section, the mean momentum can be defined as (see also (Skála,Čížek & Kapsa, 2011))…”

“…where q denotes the charge, m the mass and A is the vector potential in one dimension (see also (Skála,Čížek & Kapsa, 2011)). Using Eq.…”

“…In this chapter, we discuss quantum mechanics from the point of view of mathematical statistics and show that the most important parts of the mathematical formalism of quantum mechanics can be derived from the statistical description of results of measurement. Various aspects of this approach can be found for example in (Frieden, 1998;2004;Frieden & Soffer, 1995;Kapsa et al, 2010;Reginatto, 1998;Skála & Kapsa, 2005a;2007a;Skála,Čížek & Kapsa, 2011). One of the main differences between classical and quantum mechanics is consistent statistical description of results of measurement in quantum mechanics.…”