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As the Coulomb potential is spherically symmetric, it is best to use the results of the previous section. We replace the eigenvalue problem for the operator (114) by a family of eigenvalue problems for the ordinary differential operators [Pg.89]

The parameter k describes the angular momentum. It is the eigenvalue of the operator —K defined in (107). The quantum number k determines the total angular momentum [Pg.89]

The partial-wave operator h, does not depend on the eigenvalue of J3. This leads to the 2j + 1-fold degeneracy due to spherical symmetry. [Pg.89]

We are going to describe and to discuss the results concerning eigenfunctions and eigenvalues first, leaving some details of the calculation to later sections. [Pg.89]

It turns out that for —1 7 0 the partial-wave Dirac operator has infinitely many eigenvalues. All of them lie in the interval 0 e //, which corresponds to energies 0 i rru . The energies are [Pg.89]




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A Surface Mode Description in Relation to the MES results

ANALYSIS OF THE EXPERIMENTAL RESULTS

Action Results from the Interplay of Adhesive and Cohesive Forces

Addition Polymers Result from the Joining Together of Monomers

Advantages and disadvantages resulting from the use of neutron radiation

Algorithm and Results for the Model System

Analysing the Results of a Simulation and Estimating Errors

Analysis Step 4—Deciphering the Results

Analysis and interpretation of the results

Analysis of the Optimization Results

Analysis of the TQT Study Results

Analysis of the results

Application of Complete Energy Expression to Results Obtained from the Hard-Sphere Potential

Application of the Test Results

Atom Abstraction and Combination of the Resulting Radical with a Second Metal

Average amount of information before reporting the result

Beneficial results from the use of selectively toxic agents

Beneficial results from the use of selectivity toxic agents

Bohr-Bethe-Bloch the standard results for bare ions

Bonding and the Resulting Properties of Solids

Calculation of the result

Categories of information resulting from the design process in reactive distillation

Change in Thermodynamic Properties Resulting from the Formation of Ideal Solutions

Checking the results

Chemical Bonds to the Resulting Adhesion Strength

Chemometric Techniques for Evaluating the Results of Trace Analysis

Comparison between the results measured and simulated

Concluding Remarks Attempt to Rationalise the Results on CO Oxidation

Demethoxydaunomycin The Desired Result, but not According

Discussion of the results

Disseminating the Results, Interpretations, and Conclusions to Various Audiences

E Use of the Asymptotic Results at Intermediate Pe (or Sc)

EVALUATION OF THE NEW TUNING RULES SIMULATION RESULTS

Evaluation of the Results

Evaluation of the experimental results

Experimental Results in the Investigation of Mesophases

Experimental Results on the Kinetics of Various Reactions

Experimental Results on the Relationship between Tensile Strength and Network Structure

Experimental Results on the Swelling of Nonionic Network Systems

Experimental Results with the Vacuum Microbalance

Experimental results on the behavior of a single particle in co-axial horizontal two-impinging streams

Experiments and major results in the second stage

Experiments for final optimization of conditions and the results

Experiments of mass preparation and the results

Expression of the results

Extension of the results to arbitrary systems

Final result at the surface

Formulation of the Results in Four Dimensions

Galactosemia Is a Genetically Inherited Disease That Results from the Inability to Convert Galactose into Glucose

General Results on the Hilbert scheme

How Is the Result of a TLC Represented

Implications of the Experimental Results

Improving the properties of electrospun nanofibers experimental results

Impurities Resulting from the Synthesis Pathway

Initial Results using the Synchrotron Source and FPA

Interpretation of the Results to Explain Complex Stability Involving Hard and Soft Metal Ions

Interpreting the Results

Interpreting the experimental results for convergent-divergent nozzles

Kurtzs results consistency in the thermodynamic limit

Major results obtained in the first stage

Major results of the investigation

Major results of the model experiments

NSE Results from the Transition Regime

NSE Results on Chain Specific Effects Limiting the Rouse Dynamics

Naming the results

Numerical Solution of the Resulting Initial Value Problem

Obtaining the best results in growing sunflower plants

Overview of the Experimental Results

Overview of the Results Obtained

Perturbation theory. A comparison with results obtained in the Heitler-London approximation

Predicted results of the composite model and comparison with experiments

Presentation and Discussion of the Principal Results

Presented Results and the Model

Pressure The Result of Molecular Collisions

Prior Results and Motivation for the Survey

Processing the Results

Products The substances formed as a result

RADIOACTIVITY RESULTS FROM AN IMBALANCE OF FORCES IN THE NUCLEUS

RESULTS OF THE HARTREE-FOCK METHOD

Reflection of the Ion-Radical Step in Reaction Steric Results

Reporting the Results

Reporting the results of audits

Resulting from the Overall Detector Time Constant

Results Can Be Significantly Better for the Effort

Results Obtained from the Measurements

Results Obtained with the Equilibrium Dispersive Model

Results and Discussion Illustration of the HSAB Principle

Results and Discussion for the System of Fair Isle

Results and Discussion for the System of Kythnos

Results and Discussion for the System of Rauhelleren

Results and the Multiplet Theory

Results for HR solute in dilute solutions of the primitive cluster model

Results for the Membrane with Infinite Value of h on Both Sides

Results for the Mercury-Aqueous Solution Interface

Results for the Velocity Autocorrelation Function

Results for the emissivity

Results for the exact exchange

Results for the expanded model

Results for the normal extended service

Results for the plate

Results for the reduced model

Results for the schematic models

Results from the CJACS File Onward and Upward

Results from the Cyclizations

Results from the Microwave Pyrolysis of Plastics

Results from the Yale cold-ion spectrometer

Results from the filament model

Results from the pilot at Tilburg

Results from the study

Results of Model Calculations for the Cu-Ni System

Results of Numerical Simulations for the Basic System

Results of Studies Made with the Existing Methods

Results of surveillance for veterinary drug residues in the UK

Results of the Cosmic Run

Results of the Detector Calibration

Results of the Ethylene Polymerizations

Results of the Gas-Phase Polymerization Process Exergy Analysis

Results of the HP LDPE Process Exergy Analysis

Results of the Hartree Theory

Results of the Hydraulic Permeation Model

Results of the Normal-Coordinates

Results of the Optimisation Process

Results of the Optimization Process

Results of the Phenomenological Model

Results of the Seattle Bismuth Experiment

Results of the Self-consistent Field Method

Results of the Test Method

Results of the interview

Results of the simulation

Results of the simulation calculations

Results on the influences of various factors

Results relative to the nitrogen oxides traps

Selected illustrative results for the primitive model

Selected results for the primitive cluster model

Sensitivity Results on the Choice of Force Fields

Sensitivity of the Results

Simulation results for the conventionally-used sequential and simultaneous approaches

Skill 25.5 Design and analyze the results of an acid-base titration

Some Comments About the Experimental Results

Some Mapping Results Obtained with Photographs from the Various Gemini Satellites

Stabilisation of the Resulting Dispersion

State of the art results

Statistical analysis of the results

Summary and Perspective on the Reactivity Results

Survey of Results Obtained with the Self-Consistent Field Theory

Testing the results

The Analytical Result

The Basic System Experimental Results

The Conductivity Change That Results from Absorption of a Photon

The Debye-Huckel Approximation Results

The Experimental Results

The Final Results

The Gibbs Equation Experimental Results

The Resultant Angular Momentum

The Results of Microbial Digestion

The Results of Stress-Temperature Measurements

The clinical results

The experimental results and discussion

The interpretation of results

The major skeleton, elementary polycycles, and classification results

The prediction results with Kyte-Doolittle preference functions

The production of results

The resulting characteristic values

The subjective weighting results in a numerical scale of RSDI

The thermodynamic stability hypothesis DNA results

The thermodynamic stability hypothesis Protein results

The thermodynamic stability hypothesis RNA results

Theorematic Results for the Heisenberg Model

Theoretical Results for the Rigid Dumbbell Suspension Model

Timing of Electrical Pulses Resulting from Ion Arrivals at the MicroChannel Plate Collector

Trueness of the results

Unexpected Results Must Be Taught by, or Flow from the Patent Application

Using the Test Result

Value of the Resulting Products

Workers Get the Results of an Inspection

Writing the Results Section

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