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lucas_
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What would be the effects on the system for different values of the Hamiltonian preferred basis in Decoherence? Would it for example make the electrons higher in orbital or bands? Or what would be the exact effects?
Hamiltonian Preferred Basis is a mathematical concept used in quantum mechanics to describe the preferred basis for a quantum system. It is the basis in which the Hamiltonian operator, which represents the total energy of the system, is diagonal. This basis is also known as the energy eigenbasis.
Unlike other bases, Hamiltonian Preferred Basis is independent of time and remains constant throughout the evolution of the quantum system. It is also the most stable and predictable basis for a quantum system, making it a preferred choice for studying the dynamics of a system.
The Hamiltonian Preferred Basis is determined by finding the eigenstates and corresponding eigenvalues of the Hamiltonian operator. The eigenstates are then used as the basis vectors, and the eigenvalues represent the energy levels of the system.
Hamiltonian Preferred Basis is used in various applications in quantum mechanics, including quantum computing, quantum information theory, and quantum simulation. It is also used in understanding the dynamics of complex systems, such as molecules and atoms, and predicting their behavior.
One limitation of Hamiltonian Preferred Basis is that it is only applicable to systems that have a Hamiltonian operator. It also assumes that the system is isolated, which may not always be the case in real-world scenarios. Additionally, it does not take into account external influences or interactions with other systems.