Quantum Mechanics of Damped Systems II. Damping and Parabolic Potential Barrier

Details Quantum Mechanics of Damped Systems II. Damping and Parabolic Potential Barrier Quantum Mechanics of Damped Systems II. Damping and Parabolic Potential Barrier

2003-07-23

arxiv.org/abs/math-ph/0307047v1

J. Math. Phys. 45 (2004) 841-854

Physics

Mathematical Physics

14 pages

Scientific paper

We investigate the resonant states for the parabolic potential barrier known also as inverted or reversed oscillator. They correspond to the poles of meromorphic continuation of the resolvent operator to the complex energy plane. As a byproduct we establish an interesting relation between parabolic cylinder functions (representing energy eigenfunctions of our system) and a class of Gel'fand distributions used in our recent paper.

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