A pr 1 99 9 Harmonic oscillator well with a screened Coulombic core is quasi - exactly solvable
نویسنده
چکیده
In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V (x) = x 2 + Ze 2 /x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze 2 = if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N + 1)−st harmonic-oscillator energy E = 2N + 3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f = 0) but also a normalizable (N + 1)−plet of the further elementary the smallest multiplicities N we recommend their perturbative construction.
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