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Abstract: Operators play a substantial role in mathematical formalism of quantummechanics. However, explicit forms of the operators are usually postulated,based on the intuitive assumptions. In this study, variational principle wasapplied to the basic equation for expectation value to vary a generalized formof operator while keeping psi-function invariable. A restriction of beingexpectation value invariable, allowed one to derive all possible forms of theoperators corresponding to the conserved physical entities. As a result, it wasfound that only three distinctive forms of the conserved operators arepossible, tentatively assigned to be angular momentum-like, momentum-like andtotal energy-like operators. Surprisingly, all operators included constant, thesame one for each of the operators, therefore, making operators the quantumones. Absence of the quantization in original assumptions suggests that quantumcharacter of the operators and, therefore, the physical entities, is a directconsequence of the existence of the conservation laws.



Author: Nikolay Dementev

Source: https://arxiv.org/







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