Hemispheroidal quantum harmonic oscillator. (English) Zbl 1223.81102
Summary: A deformed single-particle shell model is derived for a hemispheroidal potential well. Only the negative parity states of the \(Z(z)\) component of the wave function are allowed, so new magic numbers are obtained. The influence of a term proportional to \(l^{2}\) in the Hamiltonian is investigated. The maximum degeneracy is reached at a superdeformed hemispheroidal prolate shape whose magic numbers are identical with those obtained at the spherical shape of the spheroidal harmonic oscillator. This remarkable property suggests an increased stability of such a distorted shape of deposited clusters when the planar surface remains opaque.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81V45 | Atomic physics |
| 78A57 | Electrochemistry |
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