  We study the properties of two-dimensional conformal field theories (CFTs)
with sine-square deformation (SSD). We show that there are no eigenstates of
finite norm for the Hamiltonian of a unitary CFT with SSD, except for the
zero-energy vacuum state $|0\rangle$. We then introduce a regularized version
of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a
unitary transformation corresponding to the Mobius quantization. The unitary
equivalence of the two Hamiltonians allows us to obtain zero-energy states of
the deformed Hamiltonian in a systematic way. The regularization also provides
a way to compute the expectation values of observables in zero-energy states
that are not necessarily normalizable.
