Related papers: Raising and lowering operators for angular momentu…
Suppose a classical electron is confined to move in the $xy$ plane under the influence of a constant magnetic field in the positive $z$ direction. It then traverses a circular orbit with a fixed positive angular momentum $L_z$ with respect…
In heavy quark effective theory, heavy mesons which contain a heavy quark (or antiquark) are classified by $s_l^{pi_l}$, i.e., the total angular momentum $s_l$ and the parity $pi_l$ of the light quark degrees of freedom around a static…
We present a control-theoretic analysis of the system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that by applying external fields with just two resonant frequencies, any desired unitary operator can…
This paper describes an integer multiplier for the orbital angular momentum (OAM) of light through the parallel implementation of multiple circular-sector transformations, whereby the cross-sectional circular shape of the OAM mode is…
Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection…
The orbital angular momentum of light, unlike spin, is an infinite-dimensional discrete variable and may hence offer enhanced performances for encoding, transmitting, and processing information in the quantum regime. Hitherto, this degree…
As a submanifold is embedded into higher dimensional flat space, quantum mechanics gives various embedding quantities, e.g., the geometric momentum and geometric potential, etc. For a particle moving on a two-dimensional sphere or a free…
We provide necessary and sufficient conditions for states to have an arbitrarily small uncertainty product of the azimuthal angle $\phi $ and its canonical moment $L_{z}$. We illustrate our results with analytical examples.
We draw attention to some tune problems in constructions of the quantum-field operators for spins 1/2 and 1. They are related to the existence of negative-energy and acausal solutions of relativistic wave equations. Particular attention is…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated…
Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct…
We consider the Schwinger's method of angular momentum addition using the SU(2) algebra with both a fermionic and a bosonic oscillator. We show that the total spin states obtained are: one boson singlet state and an arbitrary number of…
For planar integrable billiards, the eigenstates can be classified with respect to a quantity determined by the quantum numbers. Given the quantum numbers as $m, n$, the index which represents a class is $c = m\, \mbox{mod}\, k\,n$ for a…
The two-dimensional relativistic configurational $\vec r$-space is proposed and the exactly solvable finite-difference model of the harmonic oscillator in this space is constructed. The wave functions of the stationary states and the…
We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parameterized ansatz circuits…
Light beams carrying orbital angular momentum (OAM) have led to stunning applications in various fields from quantum information to microscopy. In this letter, we examine OAM from the recently discovered high-harmonic generation (HHG) in…
In this work apply the algebra of operators of quantum mechanics in the Helmholtz wave equation in cylindrical coordinates in paraxial approximation to describe the raising and lowering operators for the Laguerre-Gauss modes.
Parametrically modulated optomechanical systems have been recently proposed as a simple and efficient setting for the quantum control of a micromechanical oscillator: relevant possibilities include the generation of squeezing in the…
Harmonic wave functions for integer and half-integer angular momentum are given in terms of the Euler angles $(\theta,\phi,\psi)$ that define a rotation in $SO(3)$, and the Euclidean norm in ${\mathbb R}^3$. Following a classical work by…