Related papers: The Bicomplex Quantum Harmonic Oscillator
How does the inclusion of the gravitational potential alter an otherwise exact quantum mechanical result? This question motivates this report, with the answer determined from an edited version of problem #12 on p.273 of Ref.1. To elaborate,…
The paper focuses on various properties and applications of the homotopy operator, which occurs in the Poincar\'{e} lemma. In the first part, an abstract operator calculus is constructed, where the exterior derivative is an abstract…
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…
The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated, momentum dependent interaction…
In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order $q$-difference…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…
A wide class of q-deformed harmonic oscillators including those of Macfarlane type and of Dubna type is shown to be describable in a unified way. The Hamiltonian of the oscillator is assumed to be given by a q-deformed anti-commutator of…
A numerical method to build an orthonormal basis of properly symmetrized hyperspherical harmonic functions is developed. As a part of it, refined algorithms for calculating the transformation coefficients between hyperspherical harmonics…
Consider quantum harmonic oscillator, perturbed by an even almost-periodic complex-valued potential with bounded derivative and primitive. Suppose that we know the first correction to the spectral asymptotics $\{\Delta\mu_n\}_{n=0}^\infty$…
A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables…
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by…
We present a basis-set-free approach to the variational quantum eigensolver using an adaptive representation of the spatial part of molecular wavefunctions. Our approach directly determines system-specific representations of qubit…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
We consider an eigenvalue problem for an inverted one dimensional harmonic oscillator. We find a complete description for the eigenproblem in $C^{\infty}(\mathbb R)$. The eigenfunctions are described in terms of the confluent hypergeometric…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
An infinite dimensional system such as a quantum harmonic oscillator offers a potentially unbounded Hilbert space for computation, but accessing and manipulating the entire state space requires a physically unrealistic amount of energy.…
It is known that the anti-Wick (or standard coherent state) quantization of the complex plane produces both canonical commutation rule and quantum spectrum of the harmonic oscillator (up to the addition of a constant). In the present work,…
We revisit the problem posed by an anharmonic oscillator with a potential given by a polynomial function of the coordinate of degree six that depends on a parameter $\lambda $. The ground state can be obtained exactly and its energy…