Related papers: Raising and lowering operators for angular momentu…
In this work we study various notions of uncertainty for angular momentum in the spin-s representation of SU(2). We characterize the "uncertainty regions'' given by all vectors, whose components are specified by the variances of the three…
Restricting the states of a charged particle to the lowest Landau level introduces a noncommutativity between Cartesian coordinate operators. This idea is extended to the motion of a charged particle on a sphere in the presence of a…
The relativistic equivalent of the Schr\"odinger equation for a two particle bound state having the total angular momentum $S$ is written in the form of a Lorentz covariant set of equations (p_1^mu+p_2^mu+Omega^mu)Psi(p_1,p_2;P)…
A unified vision of the symmetric coupling of angular momenta and of the quantum mechanical volume operator is illustrated. The focus is on the quantum mechanical angular momentum theory of Wigner's 6j symbols and on the volume operator of…
Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonic wavefunctions. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical…
We revisit the problem of the uncertainty relation for angle by using quantum hydrodynamics formulated in the stochastic variational method (SVM), where we need not define the angle operator. We derive both the Kennard and…
The spherically symmetric volume operator is discussed and all its eigenstates and eigenvalues are computed. Even though the operator is more complicated than its homogeneous analog, the spectra are related in the sense that the larger…
This paper provides a class of feedback controllers that guarantee global stability of quantum angular momentum systems. The systems are in general finite dimensions and the stability is around an assigned eigenstate of observables with a…
The approach to quantum mechanics which we have used to derive the matrix treatment of spin from first principles is now employed to treat systems of compounded angular momentum. A general treatment is first given, which is then applied to…
This paper investigates origin of the extra stability associated with particular values (magic numbers) of the total angular momentum of electrons in a quantum dot under strong magnetic field. The ground-state energy, distribution functions…
In Loop Quantum Gravity, the quantum action of the volume operator is crucial in understanding quantum dynamics. In this work, we implement a generalized numerical algorithm that can compute the quantum action of the volume operator on a…
We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a Symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally…
Some of the most enduring questions in physics--including the quantum measurement problem and the quantization of gravity--involve the interaction of a quantum system with a classical environment. Two linearly coupled harmonic oscillators…
We construct creation and annihilation operators for harmonic oscillators with minimal length uncertainty relations. We discuss a possible generalization to a large class of deformations of cannonical commutation relations. We also discuss…
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is…
In this paper we consider the classical and quantum control of squeezed states of harmonic oscillators. This provides a method for reducing noise below the quantum limit and provides an example of the control of under-actuated systems in…
We study some fundamental issues related to the Hilbert space representation of quantum mechanics in the presence of a minimal length and maximal momentum. In this framework, the maximally localized states and quasi-position representation…
Spins and oscillators are foundational to much of physics and applied sciences. For quantum information, a spin 1/2 exemplifies the most basic unit, a qubit. High angular momentum spins (HAMSs) and harmonic oscillators provide multi-level…
We elaborate an approach to quantum fluctuations of angular momentum based on the diagonalization of the covariance matrix in two versions: real symmetric and complex Hermitian. At difference with previous approaches this is SU(2) invariant…
The Morse potential quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to…