Related papers: Supersymmetric Method for Constructing Quasi-Exact…
We discuss supersymmetric quantum mechanical models with periodic potentials. The important new feature is that it is possible for both isospectral potentials to support zero modes, in contrast to the standard nonperiodic case where either…
A class of spectral problems with a hidden Lie-algebraic structure is considered. We define a duality transformation which maps the spectrum of one quasi-exactly solvable (QES) periodic potential to that of another QES periodic potential.…
We introduce a method for treating soft modes within the analytical framework of the quasiharmonic equation of state. The corresponding double-well energy-displacement relation is fitted to a functional form that is harmonic in both the…
The potential energy surface (PES) of molecules with respect to their nuclear positions is a primary tool in understanding chemical reactions from first principles. However, obtaining this information is complicated by the fact that…
We propose a mechanical qubit based on buckling nanobars--a NEMS so small as to be quantum coherent.To establish buckling nanobars as legitimate candidates for qubits, we calculate the effective buckling potential that produces the…
A one-dimensional quantum mechanical model possessing mass gap, a gapless excitation, and an approximate parity doubling of energy levels is constructed basing on heuristic QCD-inspired arguments. The model may serve for illustrative…
Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has recently become possible by qubit tunneling spectroscopy (QTS). In the standard QTS experiments, an incoherent probe qubit is strongly coupled to one of the qubits…
As quantum technologies mature, the development of tools for benchmarking their ability to prepare and manipulate complex quantum states becomes increasingly necessary. A key concept, the state overlap between two quantum states, offers a…
Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the…
Calculating ground and excited states is an exciting prospect for near-term quantum computing applications, and accurate and efficient algorithms are needed to assess viable directions. We develop an excited state approach based on the…
Quasi-exactly solvable rational potentials with known zero-energy solutions of the Schro\" odinger equation are constructed by starting from exactly solvable potentials for which the Schr\" odinger equation admits an so(2,1) potential…
We give a brief overview of a simple and unified way, called the prepotential approach, to treat both exact and quasi-exact solvabilities of the one-dimensional Schr\"odinger equation. It is based on the prepotential together with Bethe…
We investigate the conditions under which systems of two differential eigenvalue equations are quasi exactly solvable. These systems reveal a rich set of algebraic structures. Some of them are explicitely described. An exemple of quasi…
A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.
This thesis is focused on some solvable quantum mechanical models and their associated symmetries.
We suggest a general ansatz for the energy-eigenstates when a complex one-dimensional PT-symmetric potential possesses real discrete spectrum. Several interesting features of PT-symmetric quantum mechanics have been brought out using this…
We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known…
The concept of entanglement and separability of quantum states is relevant for several fields in physics. Still, there is a lack of effective operational methods to characterise these features. We propose a method to certify quantum…
We have developed a new type of self-consistent scheme within the $GW$ approximation, which we call quasiparticle self-consistent $GW$ (QS$GW$). We have shown that QS$GW$ rather well describes energy bands for a wide-range of materials,…
We develop a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. $\cal PT$ symmetry may…