Showing papers on "Ladder operator published in 1983"
TL;DR: In this paper, the operator quantization is carried out of relativistic dynamical systems subjected to first class bosonic and fermionic constraints that generate an open any-rank irreducible gauge algebra.
121 citations
TL;DR: In this paper, the extension principle and R ∗ -operation are applied to derive and study a class of operator product expansions directly in the MS-scheme, and the existence of simple explicit formulae for coefficient functions and the phenomenon of perfect factorization are pointed out.
38 citations
TL;DR: In this article, the authors show that the lower bound on a continuous energy spectrum suffices t⊙ mathematically preclude the construction of a hermitian time operator canonically conjugate to the Hamiltonian.
34 citations
34 citations
TL;DR: In this article, a method for the approximate numerical solution of operator field equations on a lattice is proposed, where the solution of the operator field equation on the lattice can be expressed as
Abstract: A method is proposed for the approximate numerical solution of operator field equations on a lattice.
33 citations
21 citations
TL;DR: In this article, the perturbed ladder operators method is applied to the resolution of the perturbation in a convergent series of Hermite polynomials Hk, when V(X)=b2X2+ Sigma kCkHk(b12/X).
Abstract: The perturbed ladder operators method is applied to the resolution of the perturbed harmonic oscillator wave equation for the case where the perturbation is expandable in a convergent series of Hermite polynomials Hk, when V(X)=b2X2+ Sigma kCkHk(b12/X). It is found that the use of a Hermite polynomials basis, together with the use of binomial coefficient functions in the quantum number, greatly simplifies the determination of the perturbed ladder and factorisation functions. Thus, one obtains analytical expressions of the eigenenergies and eigenfunctions up to any order of the perturbation, without increasing intricacy. Thorough calculation has been given for a perturbing potential V(X) function even in X. As an illustrative application of the procedure, the resolution of the Schrodinger equation with a potential function V(X)=X2+ lambda X2/(1+gX2), g>0 is reinvestigated.
21 citations
20 citations
TL;DR: In this paper, a similarity transformation between the Morse oscillator and the two-dimensional harmonic oscillator is explored, which enables us to determine all ladder operators for the Morse and their associated algebra, avoiding the use of the factorization method.
Abstract: In this paper we explore a similarity transformation between the Morse oscillator and the two‐dimensional harmonic oscillator. This transformation enables us to determine in a simple and straightforward way, all ladder operators for the Morse oscillator and their associated algebra, avoiding the use of the factorization method.
16 citations
TL;DR: For the model of the harmonic oscillator in the relativistic configurational configuration, the quantum number l raising and lowering operators are found and the dynamical symmetry group is constructed by the Infeld-Hull factorization method as mentioned in this paper.
Abstract: For the model of the harmonic oscillator in the relativistic configurational
-representation the quantum number l raising and lowering operators are found and the dynamical symmetry group is constructed by the Infeld-Hull factorization method.
12 citations
TL;DR: In this article, the x → 1 behavior of the pion and nucleon structure functions is studied within the framework of the operator product expansion, and the work on the twist-4 structure functions are performed in the longitudinal operator basis, which has the advantage that all the exact information known about the operator matrix elements has been used during the transformation into this basis.
TL;DR: In this paper, the authors present a method for deriving new quantum operator formulas by carrying out the integrations within a normal product symbol, combining the properties of normal product and coherent state together.
Abstract: We present a novel method for deriving some new quantum operator formulas by carrying out the integrations within a normal product symbol. The idea underlying this method is combining the properties of normal product and of coherent state together. For example, we can deduce operator ordering theorems, the Fujiwara formula, and some disentangling theorems simply and directly. By means of this method we also get the explicit operator form and coherent state form for the Wigner function with these new forms, the wigner function's eigenstate is found and its zero point value property is discussed. Furthermore some famous quantum unitary transformations and the transformed matrix element for functional obtained conveniently. integral may be also
TL;DR: In this article, a manifestly gauge-invariant formulation of quantum mechanics is applied to a charged isotropic harmonic oscillator in a time-varying magnetic field in the magnetic dipole approximation.
Abstract: A manifestly gauge-invariant formulation of quantum mechanics is applied to a charged isotropic harmonic oscillator in a time-varying magnetic field in the magnetic dipole approximation. The energy operator for the problem is the sum of the kinetic and potential energies. The kinetic energy operator is the square of the gauge-invariant kinetic momentum operator divided by twice the mass. The energy eigenvalues and state probabilities are calculated and are shown to be the same in all gauges. In this problem there is no gauge in which the energy operator reduces to the unperturbed Hamiltonian, as there is in the electric dipole approximation. Consequently, eigenvalues of the unperturbed Hamiltonian and corresponding (gauge-dependent) state 'probabilities' are different from the gauge-invariant quantities in all gauges.
TL;DR: In this paper, the field creation operator is shown to be the Hermitian conjugate of the annihilation operator, and the commutation relations for boson (fermion) field operators are proved from the symmetry of the many-particle wave function.
Abstract: Second quantization in nonrelativistic quantum mechanics is given in a simplified way using eigenstates of the number operator. The field creation operator is shown to be the operator which adds a particle with a delta‐function wave function to the system, while the field annihilation operator removes a particle with a delta‐function wave function from the system. The field creation operator is proved to be the Hermitian conjugate of the annihilation operator. The commutation (anticommutation) relations for boson (fermion) field operators are proved from the symmetry (antisymmetry) of the many‐particle wave function. The second quantized form of one‐ and two‐particle operators is obtained from their form in wave mechanics using the definition of the field creation and annihilation operators.
TL;DR: In this article, the atomic fine and hyperfine structure parameters in a space of constant curvature have been obtained by use of a ladder operator technique, and it is found that the additional curvature contributions to the classical (flat) expressions increase with n.
Abstract: Analytical expressions of the atomic fine and hyperfine structure parameters in a space of constant curvature have been obtained by use of a ladder operator technique. It is found that the additional curvature contributions to the classical (flat) expressions increase with n.
01 Jun 1983
TL;DR: In this paper, the angular velocity operator is the angular momentum operator divided by the moment of inertia, and the time rate of change of the expectation value of the angular displacement φ is not equal to φ.
Abstract: Because of domain considerations for the z component of the angular momentum operator, the time rate of change of the expectation value of the angular displacement φ is not equal to the expectation value of the angular velocity operator. The angular velocity operator is the angular momentum operator divided by the moment of inertia. Ehrenfest’s theorem is obtained for the time rate of change of the expectation value of cos φ and sin φ.
TL;DR: The forms of the operators ν°, ν, λ − λ λ, λ + λ− λ and λ+ λ are presented in this article, where ν and ν are respectively the raising and lowering operators for ν − νν, the radial number operator, while λ is the raising operator for M, the magnitude of the angular momentum operator.
Abstract: The forms of the operators ν°, ν, λ°, λ, which enable one to write the Hamiltonian of the two‐dimensional isotropic harmonic oscillator in the form H=ℏω(2ν°ν+λ°⋅λ+1), are presented. Here ν° and ν are, respectively, the raising and lowering operators for ν°ν, the ‘‘radial’’ quantum number operator, while λ° and λ are, respectively, the raising and lowering operators for M, the magnitude of the angular momentum operator. Corresponding to this decomposition of H in the angular momentum basis are the energy eigenvalues Ekm=ℏω(2k+‖m‖+1) with k=0, 1, 2, ⋅⋅⋅ and m=0, ±1, ±2, ⋅⋅⋅. Here k is a ‘‘radial’’ quantum number, and m is a ‘‘magnetic’’ quantum number. The commutation relations satisfied by the operators ν°, ν, λ°, and λ are also presented.
TL;DR: In this paper, the projection operator method is proposed for a microscopic description of collective motions in the many-body problem, which enables us to systematically separate the motions of many-particle systems into two dynamically independent parts, without finding the intrinsic variables and also without using the method of redundant variables.
Abstract: The projection operator method is proposed for a microscopic description of collective motions in the many-body problem. This method enables us to systematically separate the motions of many-particle systems into two dynamically independent parts,i.e. the collective part and the intrinsic part, without finding the intrinsic variables and also without using the method of redundant variables. In our formalism, the intrinsic parts of many-particle systems are described as the dynamical systems with the so-called (in Dirac’s terminology) second-class constraints. It is shown that the resulting commutators among the intrinsic variables give the quantum-mechanical expressions for the corresponding Dirac brackets without the ambiguity of ordering the operator factors.
TL;DR: In this article, a density operator analysis of the particle-ejection problem in the generalized sudden approximation model with a random impulse perturbation is presented. But the model is restricted to the case in which the ejected particle is detected but its dynamical properties are not observed, and it is shown that the resultant statistical density operator may be derived from that obtained in a particle-conserving Hamiltonian-evolution linear-response model.
Abstract: A density operator analysis is made of the particle-ejection (e.g., photoionization) problem in the “generalized sudden approximation” for the case in which the ejected particle is detected but its dynamical properties are not observed. It is shown that the resultant statistical density operator may be derived from that obtained in a particle-conserving Hamiltonian-evolution linear-response model with a random impulse perturbation, and that the physical applicability of the latter model embraces the range of applicability of the former. The initial value of the statistical density operator for the above particle-ejection problem is shown to be the N – (1)-particle reduced density operator of the initial state; and the initial value of the statistical density operator for the excitations in the random impulse model is shown to be the N-particle Hermitian operator whose matrix representation is the G matrix of Garrod and Percus. The significance of the eigenvalue spectrum of these operators to the excitation properties of the system is discussed, especially for the random impulse model, where a large eigenvalue of the G matrix can signal strong preferential excitation to its corresponding particle-hole collective state, even for a random perturbation. Extensions of these ideas to excitations from states with a large eigenvalue of the two-particle reduced density operator (e.g., superconducting states) are mentioned. The The applicability of these density matrices to the description of the excitation spectrum due to a well-defined perturbation is discussed. The relationship of these time-dependent density operators to the one-particle propagator and the particle–hole propagator (polarization propagator) is established.