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On a relativistic scalar particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential
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The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed: a dependence of the angular frequency of the Klein-Gordon oscillator on the quantum numbers of the system. The meaning of this behaviour of the angular frequency is that only some specific values of the angular frequency of the Klein-Gordon oscillator are permitted in order to obtain bound state solutions. As an example, we obtain both the angular frequency and the energy level associated with the ground state of the relativistic system. Further, we analyse the behaviour of an electrically charged particle subject to the Klein-Gordon oscillator, the Coulomb potential and a linear scalar potential.
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Casimir effect for a massive scalar field confined between parallel plates with a spatially varying effective mass
A claimed exact Casimir energy for a scalar field with a quadratic position-dependent mass is derived, but the conversion from continuum to discrete transverse modes uses an unproven Landau-style measure.
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