Does hamiltonian/energy eigenstate always exist?

[kokolovehuh]

Hi all,
This may seem silly but...do energy eigenstates always exist in terms of wave functions themselves? To me, it seems they do because they always contain quantized energies. How about any hypothetical non-normalizeable wave functions?

Thanks

O.

 

[Matterwave]

Energy eigenstates do not exist for time-dependent Hamiltonians.

 

[kokolovehuh]

So you are implying all time-independent ones do? including the non-normalizable ones

 

[Matterwave]

The unnormalizable wave-functions exist mathematically, but are not physically realizable.

 

[Jazzdude]

Energy eigenstates do not exist for time-dependent Hamiltonians.

A time dependent hamiltonian DOES have an eigenstructure. However a possible eigenstate is not a stationary state.