Terms in LS coupling

2021 ◽  
pp. 203-211
Author(s):  
Geoffrey Brooker
Keyword(s):  
Wave Functions ◽  
Quantum Numbers ◽  
Correct Energy

“Terms in LS coupling” shows how quantum numbers L, S can be assigned for a given configuration of electrons. Certain values of L, S are excluded when the electrons are “equivalent”. It is shown how wave functions can be calculated for the permitted states. Those wave functions explain what went wrong with accounts discredited in Chapter 16. The correct energy-order of the states makes sense when put alongside the wave functions.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals Is two-pole’s $$\varLambda (1405)$$ one state or two?

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Zhong-Yu Wang ◽  
Hiwa A. Ahmed ◽  
C. W. Xiao
Keyword(s):  
Single Channel ◽  
Wave Functions ◽  
Riemann Sheet ◽  
Lower Mass ◽  
Composite State ◽  
Channel Interaction ◽  
Quantum Numbers ◽  
Coupled Channels ◽  
Pole Structure

AbstractTo understand the nature of two poles for the $$\varLambda (1405)$$ Λ ( 1405 ) state, we revisit the interactions of $${\bar{K}}N$$ K ¯ N and $$\pi \Sigma $$ π Σ with their coupled channels, where two-pole structure is found in the second Riemann sheet. We also dynamically generate two poles in the single channel interaction of $${\bar{K}}N$$ K ¯ N and $$\pi \Sigma $$ π Σ , respectively. Moreover, we make a further study of two poles’ properties by evaluating the couplings, the compositeness, the wave functions, and the radii for the interactions of four coupled channels, two coupled channels and the single channel. Our results show that the nature of two poles is unique. The higher-mass pole is a pure $${\bar{K}} N$$ K ¯ N molecule, and the lower-mass one is a composite state of mainly $$\pi \Sigma $$ π Σ with tiny component $${\bar{K}} N$$ K ¯ N . From our results, one can conclude that the $$\varLambda (1405)$$ Λ ( 1405 ) state may be overlapped with two different states of the same quantum numbers.

Internal Rotation Spectrum in the Ground State of cis Propionyl Fluoride

1981 ◽  
Vol 36 (12) ◽  
pp. 1327-1333
Author(s):  
F. Scappini ◽  
H. Dreizler
Keyword(s):  
Internal Rotation ◽  
Ground State ◽  
Wave Functions ◽  
Rigid Rotor ◽  
Quantum Numbers ◽  
High K ◽  
Forbidden Transitions ◽  
Low K ◽  
Rotation Spectrum

AbstractThe microwave ground state spectrum of cis propionyl fluoride has been investigated expanding, with respect to a previous study, the range of the quantum numbers of the transitions, J up to 40 and K up to 18. At low K the spectrum resembles that of an asymmetric rigid rotor, except in a number of cases where the lines are split into A, E doublets. At intermediate and high K the mixing of the if-doublet rigid rotor wave functions makes forbidden transitions appear. The results of the analysis of the methyl top internal rotation ground state splittings are: V3 = 2350 ± 11 cal/mole, ≮ (i, a) = 32.7° ±2.0°, and Iα = 3.18 ± 0.03 uÅ2.

The octupole deformation of 143Ba

2015 ◽  
Vol 24 (11) ◽  
pp. 1550081 ◽  
Author(s):  
Yong-Jing Chen ◽  
Yong-Shou Chen ◽  
Zao-Chun Gao ◽  
Ya Tu
Keyword(s):  
Experimental Data ◽  
Shell Model ◽  
Ground State ◽  
Wave Functions ◽  
Rotational Bands ◽  
Octupole Deformation ◽  
Quantum Numbers

Based on existence of the octupole deformation in the intrinsic states, the experimentally observed four rotational bands in [Formula: see text]Ba have been well reproduced by the reflection asymmetric shell model (RASM) calculations. Through the analysis of the calculated RASM wave functions, the intrinsic configuration of the observed rotational bands has been assigned as the octupole deformed neutron [Formula: see text] orbit, which is just located below the [Formula: see text] shell gap. The calculated results supported the ground state octupole deformation and the purity of the simplex quantum numbers [Formula: see text] in [Formula: see text]Ba. In addition, the calculated [Formula: see text] values are in agreement with experimental data, and further support the octupole deformation in [Formula: see text]Ba.

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

High-lying doubly excited states of He and H−: electron correlations and classification schemes

Open Physics ◽  
2005 ◽  
Vol 3 (3) ◽  
Author(s):  
Spyros Themelis
Keyword(s):  
Excited States ◽  
Wave Functions ◽  
Electron Correlations ◽  
Classification Schemes ◽  
Doubly Excited States ◽  
Quantum Numbers ◽  
Doubly Excited

AbstractHigh-lying doubly excited states of He and H− are studied and energies and intrinsic characteristics of their wave-functions are reported. Results for energies of 3Po and 1D doubly excited states associated with the hydrogenic thresholds up to N = 20 are presented and compared to available data from the literature. The classification of these doubly excited states by approximate quantum numbers is reexamined.

Collective motion in the nuclear shell model II. The introduction of intrinsic wave-functions

1958 ◽  
Vol 245 (1243) ◽  
pp. 562-581 ◽  
Keyword(s):  
Collective Motion ◽  
Permanent Deformation ◽  
Integral Form ◽  
Wave Functions ◽  
Quadrupole Moments ◽  
Rotational Model ◽  
Quantum Numbers ◽  
The Hill ◽  
Nuclear Shell

The wave functions for a number of particles in a degenerate oscillator level, classified in part I according to irreducible representations of the group U 3 , are expressed as integrals of the Hill-Wheeler type over intrinsic states. The rotational band structure which appeared in the classification is now understood, since all states of a band are shown to involve the same intrinsic state in the integral. It is possible to use the quantum number K of the intrinsic states as an additional label for the final wave functions, thus distinguishing states which, in the classification of part I, had the same values for all other quantum numbers used. The integral form for the wave functions enables simple expressions to be obtained for the quadrupole moments which resemble those of the rotational model for a permanent deformation.

The Dirac particle in the graphene dot confined within the magnetic barriers

2017 ◽  
Vol 31 (30) ◽  
pp. 1750273
Author(s):  
Weixian Yan ◽  
Kaili Zuo ◽  
Lijuan Deng
Keyword(s):  
Magnetic Fields ◽  
Dirac Particle ◽  
Wave Functions ◽  
Landau Levels ◽  
Graphene Quantum Dot ◽  
Quantum Numbers ◽  
Counting Rules ◽  
Magnetic Barriers ◽  
Analytical Expressions ◽  
The Magnetic Field

The analytical expressions for the eigenenergies and functions of the graphene quantum dot perpendicularly pierced by the different but parallel magnetic fields inside [Formula: see text] and outside [Formula: see text] dot have been derived with the ratio of the magnetic field strengths being irreducible rational [Formula: see text]. It is numerically found that the curves of eigenenergies consist of the clusters bounded by a series of the two sequential different Landau levels proportional to [Formula: see text] and [Formula: see text], respectively. The eigenenergies depend sensitively on the magnetic quantum numbers as well as the ratio of two different magnetic fields. The counting rules for the number of the valleys within the probability density of the wave functions have been established to interpret the interrelationship between the eigenenergies and wave functions. In addition, the crowding-in effect of the wave functions due to the increase of the eigenenergies is revealed.

LOW-LYING DIBARYON STATES IN A SYMMETRY ANALYSIS

2003 ◽  
Vol 18 (02n06) ◽  
pp. 414-417
Author(s):  
YUXIN LIU ◽  
JINGSHENG LI ◽  
Chengguang Bao
Keyword(s):  
Surface Structure ◽  
Structure Analysis ◽  
Symmetry Analysis ◽  
Wave Functions ◽  
Color Channel ◽  
Nodal Surface ◽  
Quantum Numbers ◽  
Color Channels

The dibaryon states as six-quark clusters of exotic QCD states are investigated in this talk. With the inherent nodal surface structure analysis, the wave functions of the six-quark clusters (in another word, the dibaryons) are classified. The contribution of the hidden color channels are discussed. The quantum numbers of the low-lying dibaryon states are obtained. The States [ΩΩ](0,0+), [ΩΩ](0,2-), [Ξ* Ω](1/2,0+), [ΞΩ](1/2,1+), [Σ* Σ*](0,4-) and the hidden color channel states with the same quantum numbers are proposed to be the candidates of dibaryons, which may be observed in experiments.

scholarly journals Annihilation rates of 3D2(2−−) and 3D3(3−−) heavy quarkonia

2017 ◽  
Vol 32 (06n07) ◽  
pp. 1750035 ◽  
Author(s):  
Tianhong Wang ◽  
Hui-Feng Fu ◽  
Yue Jiang ◽  
Qiang Li ◽  
Guo-Li Wang
Keyword(s):  
Excited States ◽  
Mass Spectra ◽  
Decay Rates ◽  
Wave Functions ◽  
Heavy Quarkonia ◽  
Relativistic Corrections ◽  
Quantum Numbers

We calculate the annihilation decay rates of the [Formula: see text] and [Formula: see text] charmonia and bottomonia by using the instantaneous Bethe–Salpeter (BS) method. The wave functions of states with quantum numbers [Formula: see text] and [Formula: see text] are constructed. By solving the corresponding instantaneous BS equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic corrections are large. The results for the [Formula: see text] channel are as follows: [Formula: see text] keV, [Formula: see text] keV, [Formula: see text] keV and [Formula: see text] keV.

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