Everything about Ground State totally explained
In
quantum mechanics, a
stationary state is an
eigenstate of a
Hamiltonian, or in other words, a state of definite energy. It is called
stationary because the corresponding probability density has no time dependence.
As an eigenstate of the Hamiltonian, a stationary state isn't subject to change or decay (to a lower energy state). In practice, stationary states are never truly "stationary" for all time. Rather, they refer to the eigenstate of a Hamiltonian where small
perturbative effects have been ignored. The language allows one to discuss the eigenstates of the unperturbed Hamiltonian, whereas the perturbation will eventually cause the stationary state to decay. The only true stationary state is the ground state.
Ground state
The
ground state of a
quantum mechanical system is its lowest-
energy state. An
excited state is any state with energy greater than the ground state. The ground state of a
quantum field theory is usually called the
vacuum state or the
vacuum.
If more than one ground state exists, they're said to be
degenerate. Many systems have degenerate ground states, for example, the
hydrogen atom. It turns out that degeneracy occurs whenever a nontrivial
unitary operator commutes with the
Hamiltonian of the system.
According to the
third law of thermodynamics, a system at
absolute zero temperature exists in its ground state; thus, its
entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect
crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero (because ln(1) = 0).
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