We present an interesting result regarding the implication of truncating the wavepacket of the harmonic oscillator. We show that disregarding the non-significant tails of a function which is the superposition of eigenfunctions of the harmonic oscillator has a remarkable consequence. Namely, there exit infinitely many different superpositions giving rise to the same function on the interval. Uni...

Using algebraic tools of supersymmetric quantum mechanics we construct classes of conditionally exactly solvable potentials being the supersymmetric partners of the linear or radial harmonic oscillator. With the help of the raising and lowering operators of these harmonic oscillators and the SUSY operators we construct ladder operators for these new conditionally solvable systems. It is found t...

We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy ET from a given initial state (qi, pi) by controlling its frequency ω,ωmin ω ωmax. A brief synopsis of optimal control theory is included and the solution for the harmonic oscillator problem is used to illustrate the theory. (Some figures in this article are in colour only in t...

We consider the forced harmonic oscillator quantized according to infinite statistics ( a special case of the ‘quon’ algebra proposed by Greenberg ). We show that in order for the statistics to be consistently evolved the forcing term must be identically zero for all time. Hence only the free harmonic oscillator may be quantized according to infinite statistics. PACS numbers: 05.30-d, 04.62+v T...

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V (x) = x 2 + Ze 2 /x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze 2 = if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N + 1)−st harmonic-oscillator ener...

An unusual type of the exact solvability is reported. It is exemplified by the Coulomb plus harmonic oscillator in D dimensions after a complexification of its Hamiltonian which keeps the energies real. Infinitely many bound states are found in closed form which generalizes the popular harmonic-oscillator states at zero charge and even parity. Apparently, the model is halfway between exact and ...

A simple non-linear network for amplitude stabilization in harmonic quadrature oscillator (QO) is analyzed. The oscillation startup conditions for QO topology with two operational amplifiers are used for amplitude adjustment by element values. A closed form expression for the amplitude setting resistance is derived. Total harmonic distortion (THD) is expressed as closed form function of the est...

We determine local Hamiltonians, Poisson structures and conserved measures for the linear ows on < 2 . We study ows around critical points as deformations of the harmonic oscillator (HO) and the free particle. In particular the damped harmonic oscillator (DHO) is Hamiltonian with respect to non-standard Poisson structures for all non-zero values of the damping constant. Treating the DHO as a de...

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrödinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Pőschl-Teller and Hulthén potentials are used as reference potentials to obtain exact energy eigenvalues and eigenf...

Harmonic oscillator in Fock space is defined. Isospectral as well as polynomiality-of-eigenfunctions preserving, translation-invariant discretization of the harmonic oscillator is presented. Dilatationinvariant and polynomiality-of-eigenfunctions preserving discretization is also given. Contribution to the Proceedings of the Conference SIDE III, Roma, Italy, May 1998 to be published by CRM Pres...