Related papers: Wave functions for quantum integrable particle sys…

We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…

For Klein-Gordon equation a consistent physical interpretation of wave functions is reviewed as based on a proper modification of the scalar product in Hilbert space. Bound states are then studied in a deep-square-well model where spectrum…

We consider two-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension. The upper fluid is bounded above by a rigid lid, and the lower fluid is bounded below by a rigid bottom. We use a…

The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinus-square potential. They are well known to be integrable and solvable. Here we extend the…

Bi-Hamiltonian hierarchies of soliton equations are derived from geometric non-stretching (inelastic) curve flows in the Hermitian symmetric spaces $SU(n+1)/U(n)$ and $SO(2n)/U(n)$. The derivation uses Hasimoto variables defined by a moving…

It is shown that the Schrodinger equation for a large family of pairs of two-dimensional quantum potentials possess wavefuctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to…

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a…

It is generally known that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological string partition function. We present two new results which make this assertion more precise:…

Six exact solutions are obtained in the general scalar-tensor theory of gravity related to spatially homogeneous wave-like models of the Universe. Wave-like space-time models allow the existence of privileged coordinate systems where the…

Wavefunction structure is analyzed for dense interacting many-boson systems using Hamiltonian $H$, which is a sum of one-body $h(1)$ and an embedded GOE of $k$-body interaction $V(k)$ with strength $\lambda$. In the first analysis, a…

Using heuristic arguments alone, based on the properties of the wavefunctions, we obtain the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator. This approach is considerably simpler and is…

I propose, as geometric structure in an internal space, a helical field that is responsible for intrinsic properties of point particles, particularly, electron. For the novel theoretical development, plasma astrophysical analogy is made…

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…

We construct the integral transform passing from the space representation to the momentum representation for the Hydrogen atom using polar spherical coordinates. The resulting radial wave functions are explicitly given in terms of complex…

We~identify the standard weighted Bergman kernels of spaces of nearly holomorphic functions, in~the sense of Shimura, on~bounded symmetric domains. This also yields a description of the analogous kernels for spaces of…

We introduce two-parameter classes of exactly-solvable novel systems whose Hamiltonian operators could be represented by tridiagonal symmetric matrices in some orthogonal bases. The associated wavefunction is written as point-wise…

In this paper we solve the one-particle Schr\"{o}dinger equation in a magnetic field whose flux lines exhibit mutual linking. To make this problem analytically tractable, we consider a high-symmetry situation where the particle moves in a…

We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and try to characterize the relevant…

A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a…

The N=2 supersymmetric extension of the Schr\"odinger-Hamiltonian with 1/r-potential in d dimension is constructed. The system admits a supersymmetrized Laplace-Runge-Lenz vector which extends the rotational SO(d) symmetry to a hidden…