Showing papers on "Ladder operator published in 1979"
TL;DR: In this article, the eigenfunctions and eigenenergies for the hydrogen atom in N dimensions were derived in simple analytic closed form, where the relation to the harmonic oscillator, the ground state energy per degree of freedom, raising and lowering operators, and the radial momentum operators were discussed.
Abstract: We derive in simple analytic closed form the eigenfunctions and eigenenergies for the hydrogen atom in N dimensions. A section is devoted to the specialization to one dimension. Comments are made on the relation to the harmonic oscillator, the ground‐state energy per degree of freedom, the raising and lowering operators, and the radial momentum operators. By particular changes of variables, the relativistic pi‐mesic atom is solved in the same functional form.
198 citations
165 citations
TL;DR: In this article, the exact, normalized, closed-form eigenfunctions for the one-dimensional Morse oscillator, as well as the raising and lowering operators, were obtained based on the classical motion of a particle.
Abstract: We obtain the exact, normalized, closed-form eigenfunctions for the one-dimensional Morse oscillator, as well as the raising and lowering operators. We next review a new method for obtaining the coherent states for arbitrary potentials, it being based on the classical motion of a particle. We apply this method to the Morse oscillator. After demonstrating that in the appropriate limit our results reduce to those for the harmonic oscillator, we obtain analytic insights into published numerical results on uncertainty products for Morse-oscillator wave packets.
125 citations
TL;DR: In this article, the inverse scattering transform used to solve the classical nonlinear Schroedinger equation may be formulated as an operator method for solving the corresponding quantum field theory (delta-function many-body problem).
Abstract: It is shown that the inverse scattering transform used to solve the classical nonlinear Schroedinger equation may be formulated as an operator method for solving the corresponding quantum field theory (delta-function many-body problem).
69 citations
TL;DR: In this paper, the determinant of the Dirac operator in a general multi-instanton background field was computed. But it was not shown how to compute determinant in the case of a general background field.
34 citations
25 citations
TL;DR: In this paper, the determination of atomic wavefunctions when the usual Euclidean flat space is substituted by a spherical 3-space is investigated, and a multipolar expansion of the bielectronic repulsion potential is given, allowing the computation of curvature-dependent bi-electronic integrals.
Abstract: The determination of atomic wavefunctions when the usual Euclidean flat space is substituted by a spherical 3-space is investigated. Introducing hyperspherical coordinates ( chi , theta , phi ) and the 'curved' form (1/R) cot chi of the Coulomb potential, 'curved hydrogenic orbitals'-solutions of the non-relativistic wave equation-are obtained using the ladder operator technique. A multipolar expansion of the bi-electronic repulsion potential is given, allowing the computation of curvature-dependent bi-electronic repulsion integrals. Some interesting features of this 'curved model', which of course gives again the usual flat results (as the radius of curvature R to infinity ), are pointed out.
18 citations
TL;DR: In this article, the authors provide evidence of a nice relationship between index theory and operator algebras within the framework of geometric measure theory by exhibiting basic examples involving one dimensional singular integral operators and expose certain connections that exist involving the principal function associated to an operator having trace class self-commutator.
Abstract: The aim of this paper is twofold: first to provide evidence of a nice relationship between index theory and operator algebras within the framework of geometric measure theory by exhibiting basic examples involving one dimensional singular integral operators; second to expose certain connections that exist involving the principal function associated to an operator having trace class self-commutator and the theory of function algebras.
14 citations
TL;DR: In this paper, the authors develop stochastic projectional schemes for constructing measurable approximations to solutions or least-squares solutions of linear random operator equations, both with closed range and with non-closed range.
Abstract: In this paper we develop stochastic projectional schemes for constructing measurable approximations to solutions or least-squares solutions of linear random operator equations. Both operators with closed range and with non-closed range are considered.
01 Sep 1979
TL;DR: In this paper, a Bravais-lattice operator is defined in one band of a solid and its eigenstates are covariantly defined Wannier functions and their eigenvalues are all the points of the Bravais lattice.
Abstract: A Bravais-lattice operator is defined in one band of a solid. Its eigenstates are covariantly defined Wannier functions and its eigenvalues are all the points of the Bravais lattice. This operator establishes a convenient phase convention for Bloch functions. The newly defined Bravais-lattice operator is conjugate to the quasimomentum and together they form a complete set of operators by means of which any one-band operator can be expressed. The Wannier functions for different bands and sites are shown to be eigenfunctions of a band index and the Bravais-lattice operators. It is shown that the one-band position operator has a discrete spectrum with the structure of a Stark ladder in solids. A $\mathrm{kq}$ representation is defined for one band which leads to symmetric coordinates for superlattices. The conjugate operators to these symmetric coordinates form the superlattice representation of McIrvine and Overhauser.
TL;DR: In this paper, all ladder operators and some recurrence relations of the matrix elements of certain group elements of SO(3), SO(2, 1), E(2), SO (2,1), E[2], SO(4, 1] and E[3] have been explicitly determined and the underlying factorizations of the second and the fourth-order linear ordinary differential equations in terms of first and second-order ladder operators have been transparently demonstrated as an extension to the Schrodinger-Infeld-Miller factorization.
Abstract: All ladder operators and some recurrence relations of the matrix elements of certain group elements of SO(3), SO(2,1), E(2), SO(4), SO(3,1), and E(3) have been explicitly determined and the underlying factorizations of the second‐ and the fourth‐order linear ordinary differential equations in terms of first‐ and second‐order ladder operators have been transparently demonstrated as an extension to the Schrodinger–Infeld–Miller factorization. These ladder operators are very useful in physical applications where the corresponding matrix elements represent certain physical transitions.
TL;DR: In this article, a closed polynomial formula for the q th component of any off-diagonal operator equivalent of order k (integer or half-integer) is derived in terms of two-dimensional harmonic oscillator creation and annihilation operators.
TL;DR: In this paper, the d = 5 operator mixing problem in the α-gauge was analyzed from the standpoint of illustrating various results in formal operator mixing theory and the anomalous dimension eigenvalue of the physical operator was shown to be explicitly gauge invariant; mixing to and between nuisance operators is α dependent and nuisance operators do not mix back to the physical sector.
TL;DR: In this paper, a reducible representation for a single para-Bose operator is presented as a linear combination of a single Bose operator and reducible Fermi operator.
TL;DR: In this article, the diagonalizability of operators occurring in linear transport theory is discussed from a general point of view, and a correct interpretation of the main result of that theory is provided.
Abstract: Diagonalizability of operators occurring in linear transport theory is discussed from a general point of view. In particular, the operator A−1T, where T is the multiplication operator in L2 (−1, 1) and A is given by a formula of the type A f = f − Σ
o
n
aj pj , is investigated. Diagonalization of this operator which is connected with one-group neutron transport is carried out in the general case that the coefficients aj are arbitrary complex numbers. Also, a peculiarity of multi-group theory, where the operator involved has a multiple continuous spectrum, is pointed out. A correct interpretation of the main result of that theory is provided.
01 Mar 1979
TL;DR: In this paper, a linear operator on a complex normed space X is considered, and its spatial numerical range V (T ) is dened as T = T + 1.
Abstract: Let T be a linear operator on a complex normed space X . Its spatial numerical range V ( T ) is denned as
TL;DR: In this article, exact finite sum representations of the angular momentum projection operator were derived for axially symmetric and non-axial symmetric cases, where the intrinsic state is axially symmetry but the azimuthal quantum number K is not equal to zero.
Abstract: Exact finite sum representations of the angular momentum projection operator in the following two cases are derived: i) when the intrinsic state is axially symmetric but the azimuthal quantum numberK is not equal to zero, ii) when the intrinsic state does not have axial symmetry. Advantages of such representations over projection via exact numerical quadrature are discussed.
01 Dec 1979
TL;DR: In this article, a unitary operator is introduced that transforms the energy operator into an operator similar to the two-body Schroedinger operator (AIP) operator, which is used in the AIP system.
Abstract: A unitary operator is introduced that transforms the energy operator into an operator similar to the two-body Schroedinger operator. (AIP)