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qsa
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Is there any derivation of the bohr model for hydrogen using Ehrenfest theorem. References are appreciated.
qsa said:Is there any derivation of the bohr model for hydrogen using Ehrenfest theorem. References are appreciated.
SpectraCat said:The Bohr model was an (incorrect) empirical model based solely on observations (as well as Coulomb's Law), so I doubt there is any "derivation" of it using the Ehrenfest theorem. Also, I am not positive, but I would guess that the Bohr model pre-dates the Ehrenfest theorem by a non-negligible amount.
dextercioby said:It's a mere coincidence that the results of Bohr 1913 were also obtained by Pauli 1925 and Schrödinger 1926, as we now know that Bohr's assumptions are invalid.
dextercioby said:Obviously he knew how the lines are distributed in both the visible (Balmer) and invisible spectrum, then he only <fine tuned> his assumptions based on the quantization idea by Planck & Einstein. But nothing more.
The Ehrenfest theorem is a fundamental principle in quantum mechanics that describes the time evolution of expectation values of observables in a quantum system. It is important because it allows us to connect the classical and quantum descriptions of a system, and provides a way to understand the behavior of quantum systems in terms of classical concepts.
The Ehrenfest theorem can be applied to the hydrogen atom by considering the expectation values of observables such as position, momentum, and energy. This allows us to gain insight into the behavior of the hydrogen atom and understand its properties in terms of classical concepts.
The mathematical expression of the Ehrenfest theorem is given by:
d<O>/dt = (1/ihbar)<[H,O]> + <dO/dt>
where <O> represents the expectation value of observable O, H is the Hamiltonian operator, [H,O] is the commutator of H and O, and <dO/dt> is the time derivative of the observable O.
The Ehrenfest theorem allows us to calculate the time evolution of expectation values of observables in the hydrogen atom, such as the position, momentum, and energy. This helps us understand how these properties change over time and how they relate to each other, providing insight into the behavior of the hydrogen atom.
Yes, the Ehrenfest theorem can be generalized to any quantum system, not just the hydrogen atom. It is a fundamental principle in quantum mechanics that applies to all systems and allows us to connect classical and quantum descriptions of a system.