Showing papers on "Ladder operator published in 1968"
TL;DR: In this paper, the distortion operator of n th kind is introduced and a set of new objects is introduced into the theory, the n th term of which is called "the distortion operator".
74 citations
TL;DR: In this paper, a self-adjoint operator satisfying an exponentiated form of the equation Na* =a*(N+I), wherea* is an arbitrary creation operator.
Abstract: Anumber operator for a representation of the canonical commutation relations is defined as a self-adjoint operator satisfying an exponentiated form of the equationNa*=a*(N+I), wherea* is an arbitrary creation operator. WhenN exists it may be chosen to have spectrum {0, 1, 2, ...} (in a direct sum of Fock representations) or {0, ±1, ±2, ...} (otherwise). Examples are given of representations having number operators, and a necessary and sufficient condition is given for a direct-product representation to have a number operator.
56 citations
TL;DR: In this paper, a new approach is presented to the question why in quantum mechanics the orbital angular momentum has integral eigenvalues only, where the components of the angular momentum are represented by self-adjoint operators L j (j = x, y, z ) on the Hilbert space h which are constructed starting from the familiar differential operators in terms of ϑ and ϕ.
18 citations
17 citations
TL;DR: In this article, the problem of obtaining the classical function which corresponds to a given quantum operator is discussed, and its application to the phase-space distribution functions and to the ordering of an operator is briefly considered.
Abstract: The problem of obtaining the classical function which corresponds to a given quantum operator is discussed. Its application to the phase-space distribution functions and to the ordering of an operator is briefly considered.
12 citations
TL;DR: In this paper, a unitary operator is constructed for spin one, which transforms the Foldy-Wouthuysen Hamiltonian βE into the laboratory system Hamiltonian found by Weaver, Hammer and Good.
Abstract: A unitary operator is constructed for spin one, which transforms the Foldy-Wouthuysen Hamiltonian βE into the laboratory system Hamiltonian found by Weaver, Hammer and Good. Some properties of the operator are given including the behavior in the massless limit.
8 citations
TL;DR: In this article, it was shown that the first two formal perturbation equations corresponding to the smallest unperturbed eigenvalue do admit solutions in the appropriate Hilbert space, which implies that the phenomenon of spectral concentration holds.
Abstract: Let the unperturbed operator be the helium-Schrodinger operator and let the perturbation be the homogeneous-electric-field operator. It is shown that the first two formal perturbation equations corresponding to the smallest unperturbed eigenvalue do admit solutions in the appropriate Hilbert space. According to general considerations this implies that for this perturbation problem, the phenomenon of spectral concentration holds.
7 citations
TL;DR: In this article, the isotopic current operator for a Dirac field in the presence of an external Yang-Mills field is examined, where the current is viewed as the limit of a well-defined operator where the points at which the Dirac fields are evaluated have been separated infinitesimally and appropriate line integrals inserted to maintain the correct gauge transformation properties.
5 citations
4 citations
3 citations
TL;DR: In this paper, the form of the bound-state operator describing the V-θ composite state is investigated and a general class of operators having the quantum numbers of the composite state are constructed.
Abstract: The form of the bound-state operator describing the V-θ composite state is investigated. A general class of operators having the quantum numbers of the composite state is constructed. By means of an asymptotic assumption and the reduction formula, the matrix elements for the V-θ composite state are calculated. It is shown that the physical properties of the composite state are independent of the form of its bound-state operator.
TL;DR: In this paper, the Schrodinger equation for the hydrogen atom separates in three coordinate systems: spherical, parabolic, and prolate spheroidal, and the separability operators associated with the separation constants for these three systems are exhibited and discussed.
Abstract: The Schrodinger equation for the hydrogen atom separates in three coordinate systems: spherical, parabolic, and prolate spheroidal. The separability operators associated with the separation constants for these three systems are exhibited and discussed. Also, for these systems, the invariance ladder operators which transform a simultaneous eigenfunction of the separability operators into a different simultaneous eigenfunction of the same energy are discussed with reference to the elements of the O4 Lie algebra. Quantization of the Kepler problem in terms of prolate spheroidal coordinates is accomplished and discussed.
TL;DR: In this paper, the authors investigated a third expansion of the unity operator, involving a subset of the set of coherent states, and applied such an expansion to the construction of a particular kind of Bargmann space, and to the problem of expanding arbitrary operators.
Abstract: In the Hilbert space of the states of one harmonic oscillator, two different expansions of the unity operator are well known; one involving the eigenstates of the number operator, and the other involving the whole set of the coherent states. In this note we investigate a third expansion of the unity operator, involving a subset of the set of the coherent states; furthermore, we apply such an expansion, to the construction of a particular kind of Bargmann space, and to the problem of expanding arbitrary operators.
TL;DR: In this article, it was shown that the integral operator of the Bethe-Salpeter equation for the three-point function in a single-mass ϕ3 boson theory in the ladder approximation is compact for all values of total energy.
Abstract: We prove that the integral operator of the Bethe-Salpeter equation for the three-point function in a single-mass ϕ3 boson theory in the ladder approximation is compact for all values of total energy.
01 Jan 1968
TL;DR: In this article, the boundary operator and coboundary operator were combined with linear algebra and network theory, leading to a precise formulation in Chapter Six of Kirchhoff's Laws, upon which all circuit theory is based.
Abstract: We now start to develop our circuit theory by combining our linear algebra and network theory. In this Chapter such a combination yields the boundary operator and coboundary operator, leading to a precise formulation in Chapter Six of Kirchhoff’s Laws, upon which all circuit theory is based.
TL;DR: In this article, the properties of the tensor components of the transition operator with respect to an arbitrary compact group are investigated, and the principal result is that as a consequence of unitarity, the transition operation always has an invariant component whose imaginary part is nonnegative.
Abstract: The properties of the tensor components of the transition operator with respect to an arbitrary compact group are investigated. The principal result is that as a consequence of unitarity the transition operator always has an invariant component whose imaginary part is nonnegative. The connection of this result with the consistency of phenomenological calculations in broken-symmetry models is discussed.