Ground state and stationary states

[Einstein Jr.]

Can you please explain the difference between ground state and stationary state? In the stationary state, are the electrons at rest inside the atom?

 

[vanhees71]

A stationary state is, by definition, a state, where nothing changes in time. In atomic physics it's the eigenstate of the Hamiltonian of the atom (usually sufficiently described as a "point like" positively charged nucleus and electrons, leading to an overall electrically neutral bound system), neglecting the coupling of the charges to the fluctuating electromagnetic field.

The ground state is the state of lowest energy, and thus it is stable also when taking the coupling to the fluctuating radiation field into account. All the other stationary states, the excited states, are in fact instable when you take the coupling to the fluctuating radiation field into account and thus emit after some time (which cannot be predicted, because this is a random process according to quantum theory) a photon leaving the atom in a lower stationary state.

 

[jtbell]

Can you please explain the difference between ground state and stationary state?

The ground state is a stationary state: the one with lowest energy. Stationary states with higher energy are excited states.

In the stationary state, are the electrons at rest inside the atom?

In a stationary state, the position probability distribution of an electron does not change with time. Nor does the momentum probability distribution. QM does not address the question of what an electron is "really doing", "inside" the probability distribution, before something happens that "measures" the position or momentum.