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Motivated by our earlier argument that the apparent large cosmological constant from quantum fluctuations is actually an artifact of not using a full quantum mechanical superposition to determine the ground state in which the universe lives…
Generalizations of the complex number system underlying the mathematical formulation of quantum mechanics have been known for some time, but the use of the commutative ring of bicomplex numbers for that purpose is relatively new. This paper…
We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in…
This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two directions. First, we refine 2-dimensional cobordisms by…
In this note, we study the potential algebra for several models arising out of quantum mechanics with generalized uncertainty principle. We first show that the eigenvalue equation corresponding to the momentum-space Hamiltonian…
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…
The one-dimensional Schrodinger equation for the potential $x^6+\alpha x^2 +l(l+1)/x^2$ has many interesting properties. For certain values of the parameters l and alpha the equation is in turn supersymmetric (Witten), quasi-exactly…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
In this paper, we search the factorizations of the shape invariant Hamiltonians with Scarf II potential. We find two classes; one of them is the standard real factorization which leads us to a real hierarchy of potentials and their energy…
A relation between the eigenvalues of an effective Hamilton operator and the poles of the $S$ matrix is derived which holds for isolated as well as for overlapping resonance states. The system may be a many-particle quantum system with…
The axioms of Quantum Mechanics require that the hamiltonian of any closed system is self-adjoint, so that energy levels are real and time evolution preserves probability. On the other hand, non-hermitian hamiltonians with…
We consider a family of quantum Hamiltonians $H_\hbar=-\hbar^2\,(d^2\!/dx^2) +V(x)$, $x\in\mathbb{R},$ $\hbar>0,$ where $V(x)=i(x^3-x)$ is an imaginary double well potential. We prove the existence of infinite eigenvalue crossings with the…
If a scalar field theory in (1+1) dimensions possesses soliton solutions obeying first order BPS equations, then, in general, it is possible to find an infinite number of related field theories with BPS solitons which obey closely related…
We consider solitonic solutions of coupled scalar systems, whose Lagrangian has a potential term (quasi-supersymmetric potential) consisting of the square of derivative of a superpotential. The most important feature of such a theory is…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We investigate domain-wall/quantum field theory correspondences in various dimensions. Our general analysis does not only cover the well-studied cases in ten and eleven dimensions but also enables us to discuss new cases like a Type…
It is shown that the eigenproblem of any $2\times 2$ matrix Hamiltonian with discrete eigenvalues is involved with a supersymmetric quantum mechanics. The energy dependence of the superalgebra marks the disparity between the deduced…
We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one- dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially…
We use a local scale invariance of a classical Hamiltonian and describe how to construct six different formulations of quantum mechanics in spaces with two time-like dimensions. All these six formulations have the same classical limit…
We consider the Stokes phenomenon for the solutions of some partial differential equations with variable coefficients in two complex variables, where initial data are holomorphic. We use the theory of (moment) summability and the theory of…