12/17/2023 0 Comments Energy time uncertainty![]() ![]() 7.3: The Schrdinger Equation The Schrdinger equation is the fundamental equation of wave quantum mechanics. We then develop a systematic presentation of our own point of view, with regard to the role of time in the quantum theory, and give a concrete example of a measurement process not satisfying the above uncertainty relation. The energy-time uncertainty principle expresses the experimental observation that a quantum state that exists only for a short time cannot have a definite energy. Secondly, the examples of measurement processes that were used to derive the above uncertainty relation are not general enough. First, it is not consistent with the general principles of the quantum theory, which require that all uncertainty relations be expressible in terms of the mathematical formalism, i.e., by means of operators, wave functions, etc. German physicist and Nobel Prize winner Werner Heisenberg created the famous uncertainty principle in 1927, stating that we cannot know both the position. ![]() We show that this conclusion is erroneous in two respects. ![]() We then criticize the main conclusion of these treatments viz., that in a measurement of energy carried out in a time interval, Δ t, there must be a minimum uncertainty in the transfer of energy to the observed system, given by Δ ( E ′ − E ) >~ h Δ t. This problem has in fact been studied by many authors and we give a summary of their treatments. A corresponding uncertainty re-lation of a very general character between the uncertainty in time and the total energy of the system is shown to exist and is discussed briey. Because time does not appear in Schrödinger's equation as an operator but only as a parameter, the time-energy uncertainty relation must be formulated in a special way. II the concept of an uncertainty in time in quantum mechanics is introduced using the notion of time-indicating variables or clock variables. ![]()
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