Iveta Semorádová

• PhD
• Czech Technical University in Prague

Diverging eigenvalues in domain truncations of Schr\"odinger operators with complex potentials are analyzed and their asymptotic formulas are obtained. Our approach also yields asymptotic formulas for diverging eigenvalues in the strong coupling regime for the imaginary part of the potential.

Anharmonic oscillator is considered using an unusual, logarithmic form of the anharmonicity. The model is shown connected with the more conventional power-law anharmonicity ∼|x|α in the limit α → 0. An efficient and user-friendly method of the solution of the model is found in the large-N expansion technique.

The large-N expansion technique is tested via an anomalous, soft-core potential which admits the tunneling through its central barrier. The precision of the approximation is found sensitive to the asymptotic component of the interaction. Once chosen in the most common harmonic-oscillator form, and once complemented by the short range part represent...

We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed.

We explore the Klein-Gordon equation in the framework of crypto-Hermitian quantum mechanics. Solutions to common problems with probability interpretation and indefinite inner product of the Klein-Gordon equation are proposed.

Linear square-well Schr\"{o}dinger equation endowed with a singular logarithmic spike in the origin is studied. The study is methodical, motivated by the problem of non-gausson states $\psi_n(x)$, $n \neq 0$ generated by nonlinear Schr\"{o}dinger equations. Once the state-dependent self-interaction term is chosen logarithmic, $\sim -g\,\ln[\psi^*_n...

Linear square-well Schr\"{o}dinger equation endowed with a singular logarithmic spike in the origin is studied. The study is methodical, motivated by the problem of non-gausson states $\psi_n(x)$, $n \neq 0$ generated by nonlinear Schr\"{o}dinger equations. Once the state-dependent self-interaction term is chosen logarithmic, $\sim -g\,\ln[\psi^*_n...

Hamiltonians that are multivalued functions of momenta are of topical interest since they correspond to the Lagrangians containing higher-degree time derivatives. Incidentally, such classes of branched Hamiltonians lead to certain not too well understood ambiguities in the procedure of quantization. Within this framework, we pick up a model that sa...

Hamiltonians that are multivalued functions of momenta are of topical interest since they correspond to the Lagrangians containing higher-degree time derivatives. Incidentally, such classes of branched Hamiltonians lead to certain not too well understood ambiguities in the procedure of quantization. Within this framework, we pick up a model that sa...

During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical consistency of the resulting models of stable quantum systems requires a reconstruction of an alternative, amended, p...

During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical consistency of the resulting models of stable quantum systems requires a reconstruction of an alternative, amended, p...

One of the most productive applications of the recent extension of applicability of unitary quantum theory to operators $H=-d^2/dx^2+V(x) \neq H^\dagger$ (where, typically, the spectrum is real but where the coordinate is not observable anymore, $x \in \mathbb{C}$) has been found in the innovative constructions of bound states even in singular pote...