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nebula009
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It doesn't seem like a time dependent hamiltonian would have stationary states, am I wrong? I've run into conflicting information.
A time dependent Hamiltonian is a mathematical operator in quantum mechanics that represents the total energy of a quantum system and how it changes over time. It is used to describe the evolution of a quantum system over time.
Stationary states, also known as energy eigenstates, are states in a quantum system where the energy of the system remains constant and does not change over time. These states are characterized by having a definite energy value and are described by the time independent Hamiltonian.
No, a time dependent Hamiltonian cannot have stationary states. This is because the time dependent Hamiltonian does not commute with the energy operator, which means that the energy of the system is not conserved and can change over time.
Time dependent Hamiltonians are used in quantum mechanics to describe the behavior of quantum systems that are subject to external forces or interactions that change over time. They are used to calculate the evolution of the quantum state and the probabilities of different energy states.
Time dependent Hamiltonians have many real-world applications, such as in quantum computing, nuclear physics, and chemical reactions. They are also used in understanding the behavior of atoms and molecules in external fields, as well as in studying the dynamics of complex systems, such as biological systems.