Can Zero Be a Valid Eigenvalue for an Eigenstate?

[582153236]

If an operator (O) acts on a function ψ and transforms the function in a scalar manner as described below, it is said to be in an eigenstate:
Oψ=kψ
in this case, O is the operator and k some scalar value.

My question is essentially if k=0, can this still be a valid eigenstate?

for example, O could be d²/dx² and ψ could be 5x; would that be an eigenstate?

 

[Dick]

If an operator (O) acts on a function ψ and transforms the function in a scalar manner as described below, it is said to be in an eigenstate:
Oψ=kψ
in this case, O is the operator and k some scalar value.

My question is essentially if k=0, can this still be a valid eigenstate?

for example, O could be d²/dx² and ψ could be 5x; would that be an eigenstate?

Sure it would. You can have eigenvectors with eigenvalue 0.