A non-unitary similarity transformation maps a ghostly two-dimensional oscillator with bounded but non-normalisable eigenstates to an isospectral Hermitian Hamiltonian whose eigenstates are normalisable.
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Ghost-Free Quantisation of Higher Time-Derivative Theories via Non-Unitary Similarity Transformations
A non-unitary similarity transformation maps a ghostly two-dimensional oscillator with bounded but non-normalisable eigenstates to an isospectral Hermitian Hamiltonian whose eigenstates are normalisable.