Related papers: Completeness of Energy Eigenfunctions for the Refl…
We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide a necessary and sufficient condition for…
Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that…
The Swanson model is an exactly solvable model in quantum mechanics with a manifestly non self-adjoint Hamiltonian whose eigenvalues are all real. Its eigenvectors can be deduced easily, by means of suitable ladder operators. This is…
In this article, we answer the following question: If the wave equation possesses bound states but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated…
We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are…
Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the…
We carry out a Dirac sea reinterpretation of a discretized version of the Hamiltonian of quantum electrodynamics (QED), and analyze the perturbed vacuum in the continuum limit. We argue that if certain operators can be shown to be the…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
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…
In this thesis, the quantum Hamilton Jacobi (QHJ) formalism is used to study various exactly solvable (ES) and quasi -exactly solvable (QES) models. Using this method, we obtain the bound state eigenvalues and the eigenfunctions for the…
The earlier treatments of Lorentz covariant harmonic oscillator have brought to light various difficulties, such as reconciling Lorentz symmetry with the full Fock space, and divergence issues with their functional representations. We…
In the present article, we describe a method of introducing the harmonic potential into the Klein-Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.
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 study the isospectrality problem for a free quantum particle confined in a ring with a junction, analyzing all the self-adjoint realizations of the corresponding Hamiltonian in terms of a boundary condition at the junction. In…
We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories,…
A very simple procedure to calculate eigenenergies of quantum anharmonic oscillators is presented. The method, exact but for numerical computations, consists merely in requiring the vanishing of the Wronskian of two solutions which are…
We study a class of quantum two-dimensional models with complex potentials of specific form. They can be considered as the generalization of a recently studied model with quadratic interaction not amenable to conventional separation of…
The possibility of a matrix product representation for eigenstates with energy and momentum zero of a general m-state quantum spin Hamiltonian with nearest neighbour interaction and periodic boundary condition is considered. The quadratic…