Classical Stat Mech with Uncertain Initial Conditions vs. Quantum

maverick_starstrider
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Hi, I was wondering if someone could point me to a textbook or easy to read paper (or website) that briefly describes/proves the differences here. What I mean is if I do classical (continuous energies) statistical mechanics where my initial state is a volume (greater than or equal to h-bar) and do classical evolution I get a certain theory. What predictions does this make that differ from quantum mechanics which is not simply a hidden-variable theory with incomplete information of the hidden variables. Thanks for the help.
 
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This is a very broad question, and it would be impossible to answer it in a single post. However, there are several resources available that can provide an overview of the differences between classical and quantum mechanics. One of the best sources is the book "Quantum Mechanics: The Theoretical Minimum" by Leonard Susskind and Art Friedman. This book provides a comprehensive introduction to both classical and quantum mechanics, and it includes a detailed discussion of the differences between the two theories. Another useful source is the book "Quantum Mechanics: A Modern Introduction" by Andrew Whitaker. This book provides an accessible introduction to quantum mechanics, and it includes several sections devoted to discussing the differences between classical and quantum mechanics. Finally, the online encyclopedia Wikipedia has a comprehensive article on the differences between classical and quantum mechanics. This article provides a good overview of the differences, as well as links to further resources for further reading. Hopefully this information is helpful in answering your question.
 
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If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!
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