Related papers: Quasi exactly solvable quantum lattice solitons
Brief introduction to the discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation…
Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported…
Several explicit examples of quasi exactly solvable `discrete' quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable Hamiltonians of one degree of freedom. These are difference analogues of the well-known…
Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki…
Matrix quasi exactly solvable operators are considered and new conditions are determined to test whether a matrix differential operator possesses one or several finite dimensional invariant vector spaces. New examples of $2\times 2$-matrix…
We consider quantum systems consisting of a linear chain of n harmonic oscillators coupled by a nearest neighbour interaction of the form $-q_r q_{r+1}$ ($q_r$ refers to the position of the $r$th oscillator). In principle, such systems are…
The original Jaynes-Cummings model is described by a Hamiltonian which is exactly solvable. Here we extend this model by several types of interactions leading to a nonhermitian operator which doesn't satisfy the physical condition of…
It is shown that the Dunkl harmonic oscillator on the line can be generalized to a quasi-exactly solvable one, which is an anharmonic oscillator with $n+1$ known eigenstates for any $n\in \N$. It is also proved that the Hamiltonian of the…
Exactly solvable Hamiltonians are useful in the study of quantum many-body systems using quantum computers. In the variational quantum eigensolver, a decomposition of the target Hamiltonian into exactly solvable fragments can be used for…
We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the…
Necessary and sufficient conditions for quantum Hamiltonians to be exactly solvable within mean-field theories have not been formulated so far. To resolve this problem, first, we define what mean-field theory is, independently of a…
We introduce a new concept of infinite quasi-exactly solvable models which are constructable through multi-parameter deformations of known exactly solvable ones. The spectral problem for these models admits exact solutions for infinitely…
By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new…
An N-dimensional position-dependent mass Hamiltonian (depending on a parameter \lambda) formed by a curved kinetic term and an intrinsic oscillator potential is considered. It is shown that such a Hamiltonian is exactly solvable for any…
In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian…
Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…
In an attempt to regularize a previously known exactly solvable model [Yang and Zhang, Eur. J. Phys. \textbf{40}, 035401 (2019)], we find yet another exactly solvable toy model. The interesting point is that while the Hamiltonian of the…
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…
A Hamiltonian is said to be quasi-exactly solvable (QES) if some of the energy levels and the corresponding eigenfunctions can be calculated exactly and in closed form. An entirely new class of QES Hamiltonians having sextic polynomial…
A few quasi-exactly solvable models are studied within the quantum Hamilton-Jacobi formalism. By assuming a simple singularity structure of the quantum momentum function, we show that the exact quantization condition leads to the condition…