Related papers: From Quantum $A_N$ (Calogero) to $H_4$ (Rational) …
The construction of rationally-extended Morse potentials is analyzed in the framework of first-order supersymmetric quantum mechanics. The known family of extended potentials $V_{A,B,{\rm ext}}(x)$, obtained from a conventional Morse…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. In this way, a physical clock with discrete…
Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found that the energy levels for this theory are real for all $\epsilon\geq0$. Here, the…
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate…
We continue the research initiated in hep-th/0607215 and apply our method of conformal automorphisms to generate various N=4 superconformal quantum many-body systems on the real line from a set of decoupled particles extended by fermionic…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
It is shown that the 3-body trigonometric G_2 integrable system is exactly-solvable. If the configuration space is parametrized by certain symmetric functions of the coordinates then, for arbitrary values of the coupling constants, the…
In this brief review, we comment on the concept of shape invariant potentials, which is an essential feature in many settings of $N=2$ supersymmetric quantum mechanics. To motivate its application within supersymmetric quantum cosmology, we…
The recently proposed PT-symmetric quantum mechanics works with complex potentials which possess, roughly speaking, a symmetric real part and an anti-symmetric imaginary part. We propose and describe a new exactly solvable model of this…
We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity, we cover all subcritical…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
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…
We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is…
We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters…
Shape invariance is an important ingredient of many exactly solvable quantum mechanics. Several examples of shape invariant ``discrete quantum mechanical systems" are introduced and discussed in some detail. They arise in the problem of…
We construct a new class of quasi-exactly solvable many-body Hamiltonians in arbitrary dimensions, whose ground states can have any correlations we choose. Some of the known correlations in one dimension and some recent novel correlations…
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…