Spectral Asymptotics of the Non‐Self‐Adjoint Harmonic Oscillator

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Pseudospectra in non-Hermitian quantum mechanics (2014, methodology): “Furthermore, it was shown in [27] that the norms of the spectral projections ofH associated with eigenvalues 2k+1 grow exponentially as k → ∞, and the exact exponential rate of growth was identified.”
On the Solvability Complexity Index, the n-pseudospectrum and approximations of spectra of operators (2011, background): “As the importance of non-Hermitian operators in physics has been established, the spectral theory of such operators has been given a substantial amount of attention [21, 23, 24, 16] (Note also that non-Hermitian spectral problems in quantum mechanics occur in the theory of Resonances [52, 40] ).”