A Textbook Of Quantum Mechanics By Mathews And Venkatesan Pdf Free 44 ##VERIFIED##
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The empirical success of quantum mechanics, as well as the clear notion of quantum complementarity put forward by Niels Bohr, gives support to the Copenhagen interpretation. More recent research has shown that the quantum mechanical wave function is a manifestation of the underlying non-local nature of quantum mechanics, which is suggested by the impossibility of measuring the actual position and velocity of a particle accurately at the same time. In particular, Einstein's objections to the wave-particle duality of matter are shown to be valid.[47]
The position-momentum uncertainty relation is a direct consequence of the non-commutability of the operators that describe position and momentum. Attempts to explain the wave-particle duality without invoking the concept of the wave function have also been attempted. In these models, the particle-wave duality is a physical feature of the system, rather than an epistemological one. A number of quantum mechanical systems with the particle-wave duality have been studied, and in some cases it was shown that certain aspects of quantum mechanics can be derived from the classical theory in certain limits. The implication of this is that some aspects of quantum mechanics may not be fundamentally quantum mechanical, but rather classical in nature. For instance, a paper by Richard Feynman[48] discusses the possibility of explaining such phenomena as the double-slit experiment without a wave function.
However, there is now a wide variety of research on trying to apply quantum mechanical ideas to relativistic models such as the Dirac equation. Some of these are research experiments, such as the measurement of the quantum hall effect, and are not intended to be applied to the classical limit. Others, such as the research on entanglement, are attempts to use quantum theory to explain a phenomena which is alleged to be beyond classical theories. The motivation for all of this is the strong point of quantum theory that it can provide an explanation of some experimental observations which cannot be explained within the classical theory.
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