A non-trivial PT-symmetric continuum Hamiltonian and its eigenstates and eigenvalues

What is it about?

Quantum mechanics uses both real and imaginary numbers, but all the quantities we measure are described by real numbers. So some rule must be imposed on the formalism of quantum mechanics to insure that its predictions for measurement are always real numbers. PT symmetry is a special kind of rule that does this, different from the usual rules of quantum mechanics. But there are very few examples of systems with PT symmetry where one can explicitly do the calculation. We have provided a simple example that is equivalent to the usual quantum mechanical harmonic oscillator.

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Why is it important?

Physicists need specific examples where they can explicitly calculate everything. PT symmetry has very few such examples. Most of the systems with PT symmetry must be treated using either computers or perturbation theory.

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