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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 858-866 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An operator analysis is presented that provides a unified treatment of the Schrödinger (S), Klein–Gordon (KG), and Dirac (D) equations with a Coulomb potential. The analysis uses energy shift operators that factorize an appropriate radial equation. This radial equation is based on standard results and a recent formulation of the Dirac–Coulomb problem [J. Y. Su, Phys. Rev. A 32, 3251 (1985)]. The shift operators yield energy eigenvalues and a formula that contains normalized, radial coordinate-space wave functions for the S, KG, and D equations. Formulas that contain expectation values for the S, KG, and D equations are obtained by applying the hypervirial theorem and the Hellmann–Feynman theorem to the radial equation.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2650-2654 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The factorization of four vector operators, D±(ω) and D±(−ω), which occur in a representation-independent, spectrum-generating algebra for the three-dimensional, isotropic harmonic oscillator in an angular momentum basis, is considered (ω is the angular frequency of the oscillator). The D±(ω) are quantum-mechanical analogs of the classical vectors (1(minus-plus)iLˆ×)Fc (ω), where Fc(ω)=−Mωr×L+pL is constant in a frame rotating with angular velocity ωLˆ. It is shown that these four vector operators can be factorized in two different ways to yield operators that, apart from their dependence on a constant of the motion (L2), are linear in either p or r. In this way 20 abstract operators are obtained. The properties of these operators are discussed: (i) Twelve are ladder operators for the quantum numbers l, and l and m, in the eigenkets ||lm〉 of L2 and Lz. In linearized, differential form six of these operators are ladder operators for the spherical harmonics in the coordinate representation, while the other six are the corresponding operators in the momentum representation. (ii) The remaining eight operators factorize linear combinations of the Hamiltonian and the dimension operator. In linearized, differential form four of these operators are ladder operators for energy and angular momentum in the radial part of the coordinate-space wave functions, while the other four are the corresponding operators in the momentum representation.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1432-2285
    Keywords: Canopy structure ; Quercus coccifera ; Photosynthesis ; Transpiration ; Simulation model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The structural characteristics of a diverse array of Quercus coccifera canopies were assessed and related to measured and computed light attenuation, proportion of sunlit foliage, foliage temperatures, and photosynthesis and diffusive conductance behavior in different canopy layers. A canopy model incorporating all components of shortwave and longwave radiation, and the energy balance, conductance, and CO2 and H2O exchanges of all leaf layers was developed and compared with measurements of microclimate and gas exchange in canopies in four seasons of the year. In the denser canopies with a leaf area index (LAI) greater than 5, there is little sunlit foliage and the diffuse radiation (400–700 nm) is attenuated to 5% or less of the global radiation (400–700 nm) incident on the top of the canopy. Foliage of this species is nonrandomly distributed with respect to azimuth angle, and within each canopy layer, foliage azimuth and inclination angles are correlated. A detailed version of the model which computed radiation interception and photosynthetic light harvesting according to these nonrandom distributions indicated little difference in whole-canopy gas exchange from calculations of the normal model, which assumes random azimuth orientation. The contributions of different leaf layers to canopy gas exchange are not only a function of the canopy microclimate, but also the degree to which leaves in the lower layers of the canopy exhibit more shade-leaf characteristics, such as low photosynthetic and respiratory capacity and maximal conductance. On cloudless days, the majority of the foliage in a canopy of 5.4 LAI is shaded —70%–90% depending on the time of year. Yet, the shaded foliage under these conditions is calculated to contribute only about one-third of the canopy carbon gain. This contribution is about the same as that of the upper 13% of the canopy foliage. Computed annual whole-canopy carbon gain and water use are, respectively, 60% and 100% greater for a canopy of 5 LAI than for one of 2 LAI. Canopy water-use efficiency is correspondingly less for the canopy of 5 LAI than for that of 2 LAI, but most of this difference is apparent during the cool months of the year, when moisture is more abundant.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1432-2285
    Keywords: Forest decline ; Photosynthetic capacity ; Picea abies ; Stomatal conductance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Routine field determination of the parameters characterizing the activity of the photosynthetic apparatus is often difficult when attached branches of tall trees have to be used for gas exchange measurement. If severed twigs could be used, determining these parameters would be greatly facilitated. Because stomatal conductance changes when twigs or leaves are detached, CO2 assimilation is usually altered. Thus, measurements made at ambient CO2 concentration fail to accurately assess the activity of the photosynthetic apparatus because photosynthetic rates greatly depend on the supply of carbon dioxide. However, when photosynthetic carboxylation reactions are saturated by increased CO2 partial pressure in the mesophyll, CO2 assimilation rates no longer depend on instantaneous stomatal conductance, as shown by gas exchange measurements of spruce (Picea abies) twigs prior to and following detachment. Because net photosynthesis following detachment at saturating CO2 remains constant for a minimum of 15 min, photosynthetic measurements of severed twigs may be reliable. This length of time is sufficient for detaching and recutting the twig, assembling a portable minicuvette system, re-establishing steady-state conditions with the gas analyser system, and reading the data over a reasonable period of time. The method described measures the maximal photosynthetic CO2 assimilation of spruce needles of a single age-class from detached spruce twigs under the following conditions: saturating light, saturating external CO2-partial pressure, standardized temperature and air humidity in the field. The method is applicable as a routine procedure to characterize the status of the photosynthetic apparatus of spruce trees that may be damaged in the process of forest decline.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1432-2285
    Keywords: Phyllodes ; Stomatal conductance ; Transpiration ; Water potential ; Acacia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary The daily course of stomatal conductance and transpiration was monitored on each separate face of vertical phyllodes of various acacias. The selected phyllodes had a north-south orientation so that one side faced eastwards and the other westwards. The principal measurements were made on Acacia longifolia and A. melanoxylon in Portugal in late summer and autumn, and additional measurements were made on A. ligulata and A. melanoxylon in Australia. In Portugal, irrespective of soil moisture status, conductance showed on early morning maximum with a subsequent gradual decline and sometimes a subsidiary peak in the late afternoon. Maximum conductances appeared to be a function of soil moisture status, whereas the decline in conductance in the late morning and afternoon was correlated with changes in phyllode-to-air vapour pressure deficits rather than changes in phyllode water status. The relationship of transpiration to phyllode water potential did not appear to be influenced by soil moisture status, although transpiration was less in drier soils and in the afternoons, this latter factor contributing to a marked hysteresis in the relationship. The opposing faces of the phyllodes exhibited a high degree of synchrony, showing parallel stomatal opening and closing, despite their large differences in irradiance. Stomatal conductance tended to be higher on the eastern faces in the morning and lower in the afternoon. In A. longifolia the daily average of relative conductance was much the same for both faces, but in A. melanoxylon that of the eastern face was higher and was retained even when the normal orientation of the phyllodes was reversed by turning them through 180°. Synchrony must be achieved by the stomata of both sides responding to common environmental or endogenous signals which are perceived by both surfaces with equal sensitivity.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1432-2285
    Keywords: Forest decline ; Picea abies ; Mineral deficiency ; Photosynthetic performance ; Air pollution
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Damage in the older needles of Norway spruce [Picea abies (L.) Karst.] in the Fichtelgebirge (NE Bavaria, FRG) appears to result primarily from nutrient imbalances rather than from direct effects of air pollutants on the mesophyll of the needles. Support for this conclusion was obtained by altering the nutrition of older needles through the removal of terminal buds on several branches from a damaged and an undamaged spruce tree in spring. Various photosynthetic parameters, as well as the chloroplast pigment and nutrient concentrations, of 1- to 3-year-old needles on manipulated branches were compared with those of branches on which the new flush was allowed to develop during the course of the growing period. Removal of terminal buds affected only the 1-year-old needles. Elimination of the new flush resulted in a higher Ca and Mn content of the needles of the undamaged tree. This treatment also resulted in an increase of the photosynthetic capacity (under saturating light and CO2 conditions), carboxylation and light use efficiency, as well as net photosynthesis under natural conditions of the 1-year-old needles on the yellow chlorotic tree. This was accompanied by higher chlorophyll concentrations and an increase in Mg, Ca, Mn, and Zn content, and no visible signs of chlorosis developed in the experiment. By contrast, the needles of twigs in which the new flush was allowed to develop exhibited reductions in mineral content in the middle of the year. This was especially true for the elements Mg and Ca, and was accompanied by needle chlorosis and a depression of the capacity of photosynthesis. Thus it appears that there is a close relationship between the development of needle damage and nutrient imbalances in spruce. The retranslocation of elements from the 1-year-old needles to the new flush seems to play a major role in the development of needle bleaching. This approach thus supports the hypothesis described above and confirms a preliminary test with a similar experimental design, which had been conducted earlier.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1432-2048
    Keywords: Chlorophyll fluorescence ; Light scattering ; Photosynthesis ; Transpiration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Carbon dioxide exchange, transpiration, chlorophyll fluorescence and light scattering of leaves of Lycopersicom esculentum, Helianthus annuus and Arbutus unedo were measured simultaneously before and after abscission of leaves. Scattering of a weak green measuring beam was used to monitor water fluxes across the thylakoid membranes of the mesophyll. When leaves were cut under water, stomata initially closed partially and then occasionally exhibited distinct regulatory oscillations. As stomata closed, light scattering decreased indicating water influx into the mesophyll. Stomatal oscillations were accompanied, with small but noticeable phase shifts, by oscillations of water fluxes at the thylakoid level. These fluxes could be distinguished from the water fluxes accompanying light-dependent ion pumping across the thylakoids by the concomitant chlorophyll fluorescence signals. The latter record energy-dependent ion fluxes in addition to redox changes of the electron-transport chain. As stomata closed partially after cutting a leaf under water, photosynthesis decreased. In Arbutus unedo and Helianthus annuus leaves, transient stomatal closure was insufficient to account for transient inhibition of photosynthesis which appeared to be brought about by transfer of an inhibitory solute through the petiole into the mesophyll. This solute also stimulated respiration in the dark. When leaves were cut in air, stomata opened transiently (Iwanoff effect) before wilting enforced closure. Photosynthesis followed the stomatal responses, increasing during opening and decreasing during closure.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1432-2048
    Keywords: Carboxylation efficiency ; Compensation point (CO2) ; Photosynthesis (temperature, humidity) ; Sclerophyll ; Transpiration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The effect of temperature on photosynthesis at constant water-vapor pressure in the air was investigated using two sclerophyll species, Arbutus unedo and Quercus suber, and one mesophytic species, Spinacia oleracea. Photosynthesis and transpiration were measured over a range of temperatures, 20–39° C. The external concentration of CO2 was varied from 340 μbar to near CO2 compensation. The initial slope (carboxylation efficiency, CE) of the photosynthetic response to intercellular CO2 concentration, the CO2 compensation point (Γ), and the extrapolated rate of CO2 released into CO2-free air (R i) were calculated. At an external CO2 concentration of 320–340 μbar CO2, photosynthesis decreased with temperature in all species. The effect of temperature on Γ was similar in all species. While CE in S. oleracea changed little with temperature, CE decreased by 50% in Q. suber as temperature increased from 25 to 34° C. Arbutus unedo also exhibited a decrease in CE at higher temperatures but not as marked as Q. suber. The absolut value of R i increased with temperature in S. oleracea, while changing little or decreasing in the sclerophylls. Variations in Γ and R i of the sclerophyll species are not consistent with greater increase of respiration with temperature in the light in these species compared with S. oleracea.
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1432-1939
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1432-1939
    Keywords: Photosynthesis model ; RuBP regeneration ; Stomatal limitation ; Arbutus
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Summary From field gas-exchange measurements on Arbutus unedo growing in Portugal, parameter values necessary to apply an analytical, physiologicallybased model of C 3 photosynthesis were obtained. The model successfully simulated measured diurnal photosynthetic responses in Arbutus during periods without water stress, under both natural and CO2-saturating conditions. The model was used to analyze those factors limiting primary productivity during each of the experimental days. Due to a large investment in ribulose bisphosphate (RuBP) regeneration capacity, irradiance was rarely limiting, even during cloudy periods, but the limitation imposed by stomatal conductance was quite large, averaging over 30%. The fact that experimental leaves were maintained in a horizontal position is at least partially responsible for these results. Possible other reasons for this apparent excess of RuBP regeneration capacity visa-vis RuBP carboxylase-oxygenase concentration are discussed.
    Type of Medium: Electronic Resource
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