The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter—e.g., elapsed time—may be determined via arbitrary data ana...

Lie-isotopic lifting of the commutation and anticommutation relations of creation-annihilation bosonic and fermionic operators is considered. Lie-isotopic generalization of the associated supersymmetry generators and of the underlying superalgebra in considering of the Lie-isotopically lifted hamiltonian of supersymmetric quantum mechanical oscillator is defined. The generalised oscillator has ...

The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic oscillator is solved in two different types of canonical transformations. The quantum form of the classical Hamiton-Jacobi theory is also employed to solve time d...

We report a high power ultrafast Airy beam source producing femtosecond pulses at multi-gigahertz (GHz) repetition rate (RR). Based on intra-cavity cubic phase modulation of an optical parametric oscillator (OPO) designed in high harmonic cavity configuration synchronous to a femtosecond Yb-fiber laser operating at 78 MHz, we have produced ultrafast 2D Airy beam at multi-GHz repetition rate thr...

In many cases the electromagnetic modes of a sphere can be obtained exactly. Special simplifications occur when the conductivity, complex permittivity, and complex permeability vary only in the radial direction, and static and time dependent examples are discussed. With quadratic or Coulomblike permittivity variations, the wave functions resemble the quantum mechanical harmonic oscillator or hy...

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 quasi exactly solvable systems, the harmonic oscillator (with/without the centrifugal potential) deformed by a sextic potential and the 1/ sin x potential de...

Characterization and suppression of noise are essential for the control harmonic oscillators in quantum regime. We measure spectrum a oscillator from low frequency to near resonance by sensing its response amplitude modulated periodic drives with qubit. Using motion trapped ion, we experimentally demonstrate two different implementations combined sensitivity 500 Hz 600 kHz. apply our method int...

Attempts to unify Gravity Theory and Quantum Field (QFT) under Loop (LQG), are diverse; a dividing line between classical quantum is sought with Schrödinger cat-state experiments. A Primordial Theory-based alternative presented, gravity-based harmonic oscillator developed. With theory applied at micro-scales gravity meso- macro-scales, this scale-gap contributes the conceptual problems associat...