Operant techniques

Fane U 1957 Description of states in quantum mechanics by density matrix and operator techniques Rev. Mod. Phys. 29 74-93... 

This procedure is then repeated after each time step. Comparison with Eq. (2) shows that the result is the velocity Verlet integrator and we have thus derived it from a split-operator technique which is not the way that it was originally derived. A simple interchange of the Ly and L2 operators yields an entirely equivalent integrator. 

As stated above, the CG coefficients can be worked out for any particular case using the raising and lowering operator techniques demonstrated above. Alternatively, as also stated above, the CG coefficients are tabulated (see, for example, Zare s book on angular momentum the reference to which is given earlier in this Appendix) for several values of j, j, and J. 

The wastewater produced in this process consists mostly of water used in cleanup and propellant conveyance and sorting operations. Techniques such as the use of activated carbon and biological treatment are being investigated for the removal of solvents and dissolved organic compounds (143). 

J. W. MausteUer, E. Tepper, and S. J. Rodgers, FUkali Metal Handling and Systems Operating Techniques, Gordon and Breach Scientific PubUshers, Inc., New York, 1967. 

Potassium Carbonate Process. The potassium carbonate process is similar to the sodium carbonate process. However, as potassium bicarbonate [298-14-6] is more soluble than the corresponding sodium salt, this process permits a more efficient absorption than the other. The equipment layout is the same and the operation technique is similar. 

There are a variety of ways of accomplishing a particular unit operation. Alternative types of process equipment have different inherently safer characteristics such as inventory, operating conditions, operating techniques, mechanical complexity, and forgiveness (i.e., the process/unit operation is inclined to move itself toward a safe region, rather than unsafe). For example, to complete a reaction step, the designer could select a continuous stirred tank reactor (CSTR), a small tubular reactor, or a distillation tower to process the reaction. 

Operational techniques and activities that are used to fulfill requirements for quality (ISO 8402). 

The most common predictive technique which is used to analyze facilities which contain new equipment or processes, or where there is an unusually high risk to personnel or the environment is the Hazard and Operability technique or HAZOP. A HAZOP study requires a team of five to ten multi-discipline personnel consisting of representatives from engineering, operations, and health, safety, and environmental staff. The... 

The improvements may need changes in operating techniques which are thought to be adequate already. 

Variable, independent An experimental factor that can be controlled (temperature, pressure, order of test, etc.) or independently measured (hours of sunshine, specimen thickness, etc.). Independent variables may be qualitative (such as a qualitative difference in operating technique) or quantitative (such as temperature, pressure, or duration). Thus, if variable A is a function of variable B, than B is the independent variable. 

The wavefunction corrections can be obtained similarly through a resolvent operator technique which will be discussed below. The n-th wavefunction correction for the i-th state of the perturbed system can be written in the same marmer as it is customary when developing some scalar perturbation theory scheme by means of a linear combination of the unperturbed state wavefunctions, excluding the i-th unperturbed state. That is ... 

In Chapters 4, 5, and 6 the Schrodinger equation is applied to three systems the harmonie oseillator, the orbital angular momentum, and the hydrogen atom, respectively. The ladder operator technique is used in each case to solve the resulting differential equation. We present here the solutions of these differential equations using the Frobenius method. 

The reason for rejecting the solution s = —(/ + 1) is actually more complicated for states with 1 = 0. I. N. Levine (1991) Quantum Chemistry, 4th edition (Prentice-HaU, Englewood Cliffs, NJ), p. 124, summarizes the arguments with references to more detailed discussions. The complications here strengthen the reasons for preferring the ladder operator technique used in the main text. 

Chapters 4, 5, and 6 discuss basic applications of importance to chemists. In all cases the eigenfunctions and eigenvalues are obtained by means of raising and lowering operators. There are several advantages to using this ladder operator technique over the older procedure of solving a second-order differ-... 

The projection-operator technique will be employed in several examples presented in the following chapter and Chapter 12. For. the quantitative interpretation of molecular spectra both electronic and vibrational, molecular symmetry plays an all-important role. The correct linear combinations of electronic wavefunctions, as well as vibrational coordinates, are formed with the aid of the projection-operator method. 

Judd, B.R. (1963) Operator Techniques in Atomic Spectroscopy, McGraw-Hill, New York. 

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