The molecular vibration-rotation Hamiltonian in the Bargmann-Hilbert space

The molecular vibration-rotation Hamiltonian of polyatomic molecules is developed in the Bargmann-Hilbert space of entire functions. The vibration-rotation eigenvectors of polyatomic molecules are described as polynomials in complex variables where the number of complex variables is equal to the number of degrees of freedom of the molecule. Simple differential operator representations are found for all rotational and vibrational operators. A special procedure is developed, in the new representation, for describing the direction cosine operators of a rigid symmetric rotor.The new basis of molecular states is shown to be very convenient for calculating energy or intensity perturbations of molecules with axial symmetry. The theoretical methods include a treatment of doubly degenerate modes of vibration.     

The molecular vibration-rotation kinetic-energy operator for general internal coordinates

The molecular kinetic-energy operator for general internal coordinates is formulated in terms of simple generalisations of the matrices A, B, α, and β of Crawford. A new matrix γ of the gradients of the translational and rotational constraints facilitates the calculation of the β matrix. It is shown that the kinetic pseudo-potential U is most conveniently calculated as an atomic sum, and results are given for valence coordinates in various types of molecules.     

The vibration-rotation fundamental of NO

The vibration-rotation fundamental of nitric oxide has been reexamined under conditions of moderately high resolution. The new measurements have been combined with earlier measurements on the pure rotation spectrum to give improved vibration-rotation constants. The main results are (in cm^?1)

     

4.

The effects of vibration-rotation interaction on the quadrupole hyperfine structure of molecular rotational levels     

M.R. Aliev  J.T. Hougen 《Journal of Molecular Spectroscopy》1984,106(1):110-123

By using a contact transformation method similar to that commonly employed when determining higher-order corrections to the harmonic oscillator and rigid rotor energy levels of molecules, analogous centrifugal distortion and anharmonic corrections to the nuclear quadrupole coupling energies have been obtained for molecules containing one quadrupolar nucleus. The J, K dependence and v, l dependence of these higher-order corrections to the quadrupole hyperfine energies can be cast in a form which is remarkably similar to the form taken for ordinary vibrational and rotational energy corrections, a result which was not evident from earlier partial treatments of this general problem. Results are obtained here for asymmetric top, symmetric top, spherical top, and linear molecules.     

5.

Derivation of the molecular vibration-rotation Hamiltonian from the Schrödinger equation for the molecular model     

James D. Louck 《Journal of Molecular Spectroscopy》1976,61(1):107-137

The vibration-rotation Hamiltonian for a polyatomic molecule is derived in the form discovered by Watson by starting with the Schrödinger equation for the N particle system comprising the molecular model.     

6.

The inversion of diatomic vibration-rotation expectation values     

James K.G. Watson 《Journal of Molecular Spectroscopy》1979,74(2):319-321

     

7.

The effective rotational hamiltonian for open-shell molecules     

Terry A. Miller 《Molecular physics》2013,111(2):105-120

A formalism for obtaining the effective rotational hamiltonian for any open-shell molecule is described. This effective hamiltonian is shown to be formed of series of irreducible tensors composed of real and fictitious angular momentum operators. The operations of these tensors may in all cases be restricted to a particular electronic state. Application of such a formalism should be particularly valuable in the interpretation of the high resolution spectra (zero-field microwave, gas-phase electron resonance, etc.) of open-shell molecules, for it follows that the experimental data may always be interpreted without explicit reference to electronic states other than that wherein the spectrum originates. Useful rules are given which determine the relevant orders of tensors in the series and the method is illustrated for the case of a ³Σ diatomic molecule.     

8.

The Multimomentum hamiltonian formalism in gauge theory     

G. Sardanashvily  O. Zakharov 《International Journal of Theoretical Physics》1992,31(8):1477-1504

We extend the jet bundle machinery of gauge theory to the multimomentum Hamiltonian formalism. This enables us to manipulate finite-dimensional momentum spaces of fields. In the framework of this formalism, time and spatial coordinates are regarded on the same footing, and a preliminary (3 + 1) splitting of a world manifold is not required. We get the canonical splitting of a multimomentum Hamiltonian form into a connection part and a Hamiltonian density.     

9.

Fourier transform emission spectroscopy: The vibration-rotation spectrum of CuH     

R.S. Ram  P.F. Bernath  J.W. Brault 《Journal of Molecular Spectroscopy》1985,113(2):269-274

The Fourier transform infrared emission spectrum of CuH was observed. The (1, 0), (2, 1), and (2, 0) vibration-rotation bands of both ⁶³CuH and ⁶⁵CuH were recorded from a copper hollow-cathode discharge in neon and hydrogen. Improved molecular constants for the v = 0, 1, and 2 levels of CuH are provided. This work is the first observation of a vibration-rotation spectrum of a metal hydride in emission.     

10.

Method for calculation of the radiation intensity in vibration-rotation bands of molecular gases for uniform path     

A. A. Kurskov  N. S. Metel'skaya 《Journal of Applied Spectroscopy》1994,61(3-4):564-568

     

11.

The Maxwell-Vlasov equations as a continuous hamiltonian system     

Philip J. Morrison 《Physics letters. A》1980,80(5-6):383-386

The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.     

12.

A modified vibration-rotation contact transformation technique     

Azam Niroomand-Rad  Paul M. Parker 《Journal of Molecular Spectroscopy》1979,75(3):454-461

A modification of the unitary operators used in conventional vibration-rotation contact transformation calculations is described and developed. It is shown that this modification leads to substantial and significant simplifications of the existing theory. The modified theoretical development is applied to the calculation of the sextic centrifugal distortion constants of asymmetric rotators, and the recent results of Aliev and Watson are duplicated.     

13.

The scales of euclidean and hamiltonian lattice QCD     

Anna Hasenfratz  Péter Hasenfratz 《Nuclear Physics B》1981,193(1):210-220

Our earlier result on Λ_{F.g.^MOM/ΛEucl.^latt.} is confirmed by recalculating this ratio using the background field method. The relation between the scales of hamiltonian and euclidean SU(N) lattice gauge theory is also determined. We obtained

. It is in strong disagreement with the numbers previously used in the literature. It is argued that the strong coupling expansions for the string tension should be carefully reanalyzed.     

14.

An exactly solvable anharmonic Bohr hamiltonian and its equivalent boson hamiltonian     

J.N. Ginocchio 《Nuclear Physics A》1982,376(3):438-450

The eigenenergies and eigenfunctions of the bound states of an anharmonic quadrupole oscillator are derived in closed form. An interacting boson model hamiltonian is found which has the same eigenspectrum.     

15.

The use of cubic splines in vibration-rotation problems of diatomic molecules     

Pietro Cremaschi 《Molecular physics》2013,111(4):759-768

Vibration-rotation energies of diatomic molecules are computed in a basis of cubic splines using a series expansion of the centrifugal potential instead of its fitting representation. The vibrational continuum wavefunctions can be evaluated in a mixed basis set, as the spline fitting technique previously used for the electronic potential makes the analytical integration of the new functions possible. The same fitting algorithm suggests a fast method for defining approximately the best locations of the knots to be used in the least squares spline representation of the potential.     

16.

Many-time hamiltonian gravitation theory     

C. Teitelboim 《Physics letters. [Part B]》1975,56(4):376-378

It is shown that given any “good” coordinate condition in Hamiltonian general relativity one can construct an associated many-time formulation in which the constraints can be solved for some of the momenta as functionals of the remaining canonical variables. Since good coordinate conditions appear to be available for both open and closed spaces it follows that the functional wave equation for general relativity can be always put in a Tomonaga-Schwinger form. The implications of this result and some open problems are briefly discussed.     

17.

High-resolution vibration-rotation spectroscopy of fluoroform-d     

Zhu Qingshi  J.I. Steinfeld 《Journal of Molecular Spectroscopy》1981,89(2):405-412

The vibration-rotation spectrum of the ν₂ and ν₅ fundamentals of CDF₃ have been recorded using a Nicolet 7199 Fourier transform infrared spectrometer; in addition the Q branch and several subbands of each of these transitions have been investigated using a tunable semiconductor diode laser spectrometer. The Q branch and the K structure in several P(J) and R(J) subbands of ν₂, and in several Q branches of ν₅, are resolved and assigned for the first time. Constants derived for these bands are (in cm^?1) ν₂ = 1111.1823₆, B₂ = 0.32928₂, A₂ = 0.18872₂, α₂^B = 16.44₅ × 10^?4, α₂^B ? α₂^A = 12.43₅ × 10^?4, D₀^j = 3.7₃ × 10^?7, D₂^J = 4.8₃ × 10^?7; ν₅ = 975.39₁, B₅ = 0.33062, A₅ = 0.18887, α₅^B = 2.83₁ × 10^?4, α₅^A = 2.4₃ × 10^?4, ζ₅ = 0.736, D₅^J ? D₀^J = 1.2₂ × 10^?8. Some of these constants are nearly 100 times more precise than those reported in previous work.     

18.

Phipps's lagrangian and hamiltonian     

M. A. Bueno 《Foundations of Physics Letters》1994,7(4):393-400

In this work it is derived Phipps's Lagrangian function and Phipps's Hamiltonian function. This allows the utilization of Phipps's interaction in the Lagrangian and Hamiltonian frameworks.Dedicated to Thomas E. Phipps, Jr. on the occasion of his 70th birthday (1995).     

19.

Stochastic hamiltonian dynamical systems     

Joan-Andreu Lázaro-Camí  Juan-Pablo Ortega 《Reports on Mathematical Physics》2008,61(1):65-122

     

20.

The effective hamiltonian and spectra of the Op shell     

H. Dirim  J.P. Elliott  J.A. Evans 《Nuclear Physics A》1975,244(2):301-314

The effective Hamiltonian for the Op shell has been calculated up to second order using modified Sussex matrix elements. The resulting spectra and binding energies are compared with experiment and the role of the effective three-body interaction is discussed.     

Constant		$\text{v = 0}$		$\text{v = 1}$
ν		0		1875.972 ± 0.001
$\text{A}{}_{\mathrm{<mtext>eff</mtext>}}\text{= A + (0 +}\text{1}\text{2}\text{p)}$		123.1393 ± 0.0030		122.8935 ± 0.0042
$\text{B}{}_{\mathrm{<mtext>eff</mtext>}}\text{= B ?}\text{1}\text{2}\text{q}$		1.696115 ± 0.000011		1.678544 ± 0.000032

The effects of vibration-rotation interaction on the quadrupole hyperfine structure of molecular rotational levels

By using a contact transformation method similar to that commonly employed when determining higher-order corrections to the harmonic oscillator and rigid rotor energy levels of molecules, analogous centrifugal distortion and anharmonic corrections to the nuclear quadrupole coupling energies have been obtained for molecules containing one quadrupolar nucleus. The J, K dependence and v, l dependence of these higher-order corrections to the quadrupole hyperfine energies can be cast in a form which is remarkably similar to the form taken for ordinary vibrational and rotational energy corrections, a result which was not evident from earlier partial treatments of this general problem. Results are obtained here for asymmetric top, symmetric top, spherical top, and linear molecules.     

Derivation of the molecular vibration-rotation Hamiltonian from the Schrödinger equation for the molecular model

The vibration-rotation Hamiltonian for a polyatomic molecule is derived in the form discovered by Watson by starting with the Schrödinger equation for the N particle system comprising the molecular model.     

The effective rotational hamiltonian for open-shell molecules

A formalism for obtaining the effective rotational hamiltonian for any open-shell molecule is described. This effective hamiltonian is shown to be formed of series of irreducible tensors composed of real and fictitious angular momentum operators. The operations of these tensors may in all cases be restricted to a particular electronic state. Application of such a formalism should be particularly valuable in the interpretation of the high resolution spectra (zero-field microwave, gas-phase electron resonance, etc.) of open-shell molecules, for it follows that the experimental data may always be interpreted without explicit reference to electronic states other than that wherein the spectrum originates. Useful rules are given which determine the relevant orders of tensors in the series and the method is illustrated for the case of a ³Σ diatomic molecule.     

The Multimomentum hamiltonian formalism in gauge theory

We extend the jet bundle machinery of gauge theory to the multimomentum Hamiltonian formalism. This enables us to manipulate finite-dimensional momentum spaces of fields. In the framework of this formalism, time and spatial coordinates are regarded on the same footing, and a preliminary (3 + 1) splitting of a world manifold is not required. We get the canonical splitting of a multimomentum Hamiltonian form into a connection part and a Hamiltonian density.     

Fourier transform emission spectroscopy: The vibration-rotation spectrum of CuH

The Fourier transform infrared emission spectrum of CuH was observed. The (1, 0), (2, 1), and (2, 0) vibration-rotation bands of both ⁶³CuH and ⁶⁵CuH were recorded from a copper hollow-cathode discharge in neon and hydrogen. Improved molecular constants for the v = 0, 1, and 2 levels of CuH are provided. This work is the first observation of a vibration-rotation spectrum of a metal hydride in emission.     

The Maxwell-Vlasov equations as a continuous hamiltonian system

The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion.     

A modified vibration-rotation contact transformation technique

A modification of the unitary operators used in conventional vibration-rotation contact transformation calculations is described and developed. It is shown that this modification leads to substantial and significant simplifications of the existing theory. The modified theoretical development is applied to the calculation of the sextic centrifugal distortion constants of asymmetric rotators, and the recent results of Aliev and Watson are duplicated.     

The scales of euclidean and hamiltonian lattice QCD

Our earlier result on Λ_{F.g.^MOM/ΛEucl.^latt.} is confirmed by recalculating this ratio using the background field method. The relation between the scales of hamiltonian and euclidean SU(N) lattice gauge theory is also determined. We obtained

. It is in strong disagreement with the numbers previously used in the literature. It is argued that the strong coupling expansions for the string tension should be carefully reanalyzed.     

An exactly solvable anharmonic Bohr hamiltonian and its equivalent boson hamiltonian

The eigenenergies and eigenfunctions of the bound states of an anharmonic quadrupole oscillator are derived in closed form. An interacting boson model hamiltonian is found which has the same eigenspectrum.     

The use of cubic splines in vibration-rotation problems of diatomic molecules

Vibration-rotation energies of diatomic molecules are computed in a basis of cubic splines using a series expansion of the centrifugal potential instead of its fitting representation. The vibrational continuum wavefunctions can be evaluated in a mixed basis set, as the spline fitting technique previously used for the electronic potential makes the analytical integration of the new functions possible. The same fitting algorithm suggests a fast method for defining approximately the best locations of the knots to be used in the least squares spline representation of the potential.     

Many-time hamiltonian gravitation theory

It is shown that given any “good” coordinate condition in Hamiltonian general relativity one can construct an associated many-time formulation in which the constraints can be solved for some of the momenta as functionals of the remaining canonical variables. Since good coordinate conditions appear to be available for both open and closed spaces it follows that the functional wave equation for general relativity can be always put in a Tomonaga-Schwinger form. The implications of this result and some open problems are briefly discussed.     

High-resolution vibration-rotation spectroscopy of fluoroform-d

The vibration-rotation spectrum of the ν₂ and ν₅ fundamentals of CDF₃ have been recorded using a Nicolet 7199 Fourier transform infrared spectrometer; in addition the Q branch and several subbands of each of these transitions have been investigated using a tunable semiconductor diode laser spectrometer. The Q branch and the K structure in several P(J) and R(J) subbands of ν₂, and in several Q branches of ν₅, are resolved and assigned for the first time. Constants derived for these bands are (in cm^?1) ν₂ = 1111.1823₆, B₂ = 0.32928₂, A₂ = 0.18872₂, α₂^B = 16.44₅ × 10^?4, α₂^B ? α₂^A = 12.43₅ × 10^?4, D₀^j = 3.7₃ × 10^?7, D₂^J = 4.8₃ × 10^?7; ν₅ = 975.39₁, B₅ = 0.33062, A₅ = 0.18887, α₅^B = 2.83₁ × 10^?4, α₅^A = 2.4₃ × 10^?4, ζ₅ = 0.736, D₅^J ? D₀^J = 1.2₂ × 10^?8. Some of these constants are nearly 100 times more precise than those reported in previous work.     

Phipps's lagrangian and hamiltonian

In this work it is derived Phipps's Lagrangian function and Phipps's Hamiltonian function. This allows the utilization of Phipps's interaction in the Lagrangian and Hamiltonian frameworks.Dedicated to Thomas E. Phipps, Jr. on the occasion of his 70th birthday (1995).     

The effective hamiltonian and spectra of the Op shell

The effective Hamiltonian for the Op shell has been calculated up to second order using modified Sussex matrix elements. The resulting spectra and binding energies are compared with experiment and the role of the effective three-body interaction is discussed.