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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…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly…
We introduce a scheme to reconstruct arbitrary states of networks composed of quantum oscillators--e.g., the motional state of trapped ions or the radiation state of coupled cavities. The scheme uses minimal resources, in the sense that it…
We investigate a generalized quantum perceptron architecture characterized by an oscillating activation function with a tunable frequency ranging from zero to infinity. Employing analytical techniques from statistical mechanics, we derive…
Quantum state purification, which operates not by identifying and correcting specific errors but by repeatedly projecting multiple noisy copies onto special subspaces, provides a syndrome-free alternative to quantum error correction.…
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all…
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive…
The existence of quantum tunneling opens the possibility of a sudden spatial relocalization of a system after a minor modification of its parameters. Such a quantum analogue of the Thom's classical catastrophe would manifest itself,…
The resonant state expansion, a rigorous perturbation theory, recently developed in electrodynamics, is applied to non-relativistic quantum mechanical systems in one dimension. The method is used here for finding the resonant states in…
The resulting stationary states and scattering properties of an effective potential brought about by embedding a quantum well in another well are investigated in this work. The composite well system is constructed via a superposition of…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of…
We consider the situation of a two-level quantum system undergoing a continuous indirect measurement, giving rise to so-called "quantum trajectories". We first describe these quantum trajectories in a physically realistic discrete-time…
We show that a parametrically coupled qubit can be used to fully reconstruct the quantum state of a harmonic oscillator, even when both systems are subject to decoherence. By controlling the coupling strength of the qubit over time, the…
Classical and nonclassical states of quantum complex oscillators with real spectrum are presented. Such states are bi-orthonormal superpositions of $n+1$ energy eigenvectors of the system with binomial-like coefficients. For large values of…
An alternative perturbative expansion in quantum mechanics which allows a full expression of the scaling arbitrariness is introduced. This expansion is examined in the case of the anharmonic oscillator and is conveniently resummed using a…
One of the most widely problem studied in quantum mechanics is of an infinite square-well potential. In a minimal-length scenario its study requires additional care because the boundary conditions at the walls of the well are not well…