相关论文: Exact solutions for semirelativistic problems with…
Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in a discrete basis and an eigenvalue problem is reduced to solving a three term…
In this paper, we solve the eigenvalues and eigenvectors problem with Bohr collective Hamil- tonian for triaxial nuclei. The ? beta part of the collective potential is taken to be equal to Hulth?en potential while the gamma part is defined…
Analytical solutions of the Bohr Hamiltonian are obtained in the $\gamma$-unstable case, as well as in an exactly separable rotational case with $\gamma\approx 0$, called the exactly separable Morse (ES-M) solution. Closed expressions for…
In this paper we study a non-homogeneous eigenvalue problem involving variable growth conditions and a potential $V$. The problem is analyzed in the context of Orlicz-Sobolev spaces. Connected with this problem we also study the…
We present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty. By requiring the self-adjointness property of the Hamiltonian, we completely determine the…
The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…
We establish the global existence of forward self-similar solutions to the two-dimensional incompressible Navier-Stokes equations for any divergence-free initial velocity that is homogeneous of degree $-1$ and locally H\"older continuous.…
We present a method for obtaining the quasi-exact solutions of the Rabi Hamiltonian in the framework of the asymptotic iteration method. The energy eigenvalues, the eigenfunctions and the associated Bender-Dunne orthogonal polynomials are…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its…
We investigate the analytical solution of a new exactly solvable non-central potential of $V(r,\theta) = D({\frac{r - a}{r}})^2+{\frac{\beta}{r^2\sin^2 \theta}}+{\frac{\gamma \cos \theta}{r^2\sin^2 \theta}}$ type, which may be called as the…
We make use of a recently developed method to, not only obtain the exactly known eigenstates and eigenvalues of a number of quasi-exactly solvable Hamiltonians, but also construct a convergent approximation scheme for locating those levels,…
The conventional Hamiltonian $H= p^2+ V_N(x)$, where the potential $V_N(x)$ is a polynomial of degree $N$, has been studied intensively since the birth of quantum mechanics. In some cases, its spectrum can be determined by combining the WKB…
A sixth order quadrupole boson Hamiltonian is treated through a time dependent variational principle approach choosing as trial function a coherent state with respect to zeroth $b^{\dagger}_0$ and second $b^{\dagger}_2+b^{\dagger}_{-2}$…
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…
The eigenvalue problem for radial potentials is considered in a space whose spatial coordinates satisfy the SU(2) Lie algebra. As the consequence, the space has a lattice nature and the maximum value of momentum is bounded from above. The…
Central D-dimensional Hamiltonians $H = p^2 + a |\vec{r}|^2 + b |\vec{r}|^4 + >... + z |\vec{r}|^{4q+2}$ (where z=1) are considered in the limit $D \to \infty$ where numerical experiments revealed recently a new class of q-parametric…
We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and…
Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be…
The spectrum of a one-dimensional Hamiltonian with potential $V(x)=ix^2$ for negative $x$ and $V(x)=-ix^2$ for positive $x$ is analyzed. The Schr\"odinger equation is algebraically solvable and the eigenvalues are obtained as the zeros of…