Abstract
Using the functional analysis method, we present the exact solutions of the double ring-shaped oscillator (DRSO) potential with certain parity in the cylindrical coordinates. Such a quantum system is separated to two differential equations, i.e. a one-dimensional harmonic oscillator plus an inverse square term and a two-dimensional harmonic oscillator plus an inverse square term. The key point is how to find the adapted symmetrical solutions of the one-dimensional harmonic oscillator plus an inverse square term at the singular point z = 0. The obtained results are compared with those in the spherical coordinates. We also explore intimate connections ET(ip) =-ET(p) and Ez(iz) =-Ez(z) by substituting p → ip and z → iz.
Original language | English |
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Article number | 1550200 |
Journal | Modern Physics Letters A |
Volume | 30 |
Issue number | 39 |
DOIs | |
State | Published - 21 Dec 2015 |
Keywords
- Double ring-shaped oscillator
- adapted symmetrical solutions
- functional analysis method
- parity