Stationary State Properties
As shown above, a stationary state is not mathematically constant:
However, all observable properties of the state are in fact constant. For example, if represents a simple one-dimensional single-particle wavefunction, the probability that the particle is at location x is:
which is independent of the time t.
The Heisenberg picture is an alternative mathematical formulation of quantum mechanics where stationary states are truly mathematically constant in time.
As mentioned above, these equations assume that the Hamiltonian is time-independent. This means simply that stationary states are only stationary when the rest of the system is fixed and stationary as well. For example, a 1s electron in a hydrogen atom is in a stationary state, but if the hydrogen atom reacts with another atom, then the electron will of course be disturbed.
Read more about this topic: Stationary State
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