By Carl Bender and others

The non-Hermitian PT-symmetric quantum-mechanical Hamiltonian *H=p^2+x^2(ix)^\epsilon* has real, positive, and discrete eigenvalues for all *\epsilon\geq 0*. These eigenvalues are analytic continuations of the harmonic-oscillator eigenvalues *E_n=2n+1* (n=0, 1, 2, 3, ...) at *\epsilon=0*. However, the harmonic oscillator also has negative eigenvalues *E_n=-2n-1* (n=0, 1, 2, 3, ...), and one may... Show more

March 29, 2012

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Negative-energy PT-symmetric Hamiltonians

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