Related papers: A Solvable Deformation of Quantum Mechanics
In this paper we quantize the $N$-dimensional classical Hamiltonian system $H= \frac{|q|}{2(\eta + |q|)} p^2-\frac{k}{\eta +|q|}$, that can be regarded as a deformation of the Coulomb problem with coupling constant $k$, that it is smoothly…
The $N$-dimensional quantum Hamiltonian $ \hat{H} = -\frac{\hbar^2 {|\mathbf{q} } | }{2(\eta +| {\mathbf{q}} |)} {\mathbf{\nabla}}^2 - \frac{k}{\eta + |{\mathbf{q}} |} $ is shown to be exactly solvable for any real positive value of the…
We study the spectral problems associated with the finite-difference operators $H_N = 2 \cosh(p) + V_N(x)$, where $V_N(x)$ is an arbitrary polynomial potential of degree $N$. These systems can be regarded as a solvable deformation of the…
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…
This paper proposes to broaden the canonical formulation of quantum mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the Hamiltonian, where $\dagger$ represents the mathematical operation of complex conjugation and matrix…
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…
Motivated by $T\bar T$, we introduce and study a wide class of solvable deformations of quantum-mechanical theories. These deformations map the Hamiltonian to a function of itself. We solve these theories by computing all finite-temperature…
Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are…
Quantum Hamilton-Jacobi quantization scheme uses the singularity structure of the potential of a quantum mechanical system to generate its eigenspectrum and eigenfunctions, and its efficacy has been demonstrated for several well known…
A novel analytically solvable deformed Woods-Saxon potential is investigated by means of the Supersymmetric Quantum Mechanics. Hamiltonian hierarchy method and the shape invariance property are used in the calculations. The energy levels…
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional $N=2$ supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra.…
Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to $N_f$ Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a…
The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…
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…
The Schrodinger variational approach (1926) to quantization of the natural Hamilton mechanics in $2n$-dimensional phase space is revised in the modern paradigm of quantum mechanics in application to the system the Hamilton function of which…
We study the deformation quantisation (Moyal quantisation) of general constrained Hamiltonian systems. It is shown how second class constraints can be turned into first class quantum constraints. This is illustrated by the O(N) non-linear…
The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now…
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…
In this thesis the quantum Hamilton - Jacobi (QHJ) formalism is used for (i) potentials which exhibit different spectra for different ranges of the potential parameters, (ii) exactly solvable (ES) periodic potentials (iii) quasi - exactly…
Known shape-invariant potentials for the constant-mass Schrodinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its…