How to solve self-consistent equations?

If x is the object you wish to solve, you formulate the self-consistent problem in the form x = F(x) and then solve the iteration xn+1 = F(xn). Here F could be, e.g., a Hamiltonian that has some terms whose evaluation requires you to solve a (typically linear) subproblem for a fixed xn.

What is a self-consistent equation?

For semiconductors equations, it usually refers to the solution obtained by a numerical method. It means that the carrier density profile is consistent with the potential, in other words, the obtained solution satisfies all the equations of your system (Poisson and continuity).

What is self-consistent?

: having each part logically consistent with the rest.

Is personality self-consistent?

The third tenet of Adlerian theory is: Personality is unified and self-consistent. Thus, individual psychology insists on the fundamental unity of personality and the notion that inconsistent behavior does not exist. Thoughts, feelings, and actions are all directed toward a single goal and serve a single purpose.

What does self-consistent field mean?

the interaction, averaged in a certain way, between a given particle and the other particles of a quantum-mechanical system consisting of many particles. Consequently, each particle is not located in a definite state and cannot be described by means of its own one-particle wave function. …

What is self consistency bias?

Self-consistency bias is the commonly held idea that we are more consistent in our attitudes, opinions, and beliefs than we actually are, i.e. being unable to see the changes in your thoughts/opinions because you’re sure you’ve always thought the same way. There are many different types of memory biases.

What is consistency theory?

When the relationship between intrapsychic processes and states are harmonious, there is a state of consistency. The human mental system strives to avoid inconsistency and develops various mechanisms to move from a dissonant, inconsistent state to a more harmonious state.

What is self-consistent electric field?

the interaction, averaged in a certain way, between a given particle and the other particles of a quantum-mechanical system consisting of many particles.

What is the meaning of self consistency?

What is the consistency theory?

What is consistency principle example?

Example of Consistency Principle If the business entity follows the straight-line method of depreciation. Another Example is Business entity has been following the LIFO method for valuation of inventory. LIFO accounting means inventory acquired at last would be used up or sold first.

How is self consistency used in Poisson equation?

Self consistency deals with a coupled solution of Schrodinger and Poisson equation. Charge distribution is calculated from the wave functions calculated using Schrodinger equation. Next this charge distribution is put into Poisson eqn to predict the potential distribution which is again used in Sch eqn.

How to find a self consistent Schrodinger and Poisson solution?

The equations used and the iterative procedure for ob- taining self-consistent Schrodinger and Poisson solutions is described in Sec. II. Section HI describes the matrix trans- formation used to preserve the symmetry of the discretized Schrodinger equation and the Newton method to solve the Poisson equation.

Which is the correct solution for the Schrodinger equation?

Real space is divided into discrete mesh points and the wave function is solved within those discrete spacings. Solving the differential equation within each mesh spacing results in a vector solution for t/J, and a matrix formulation of the Schrodinger equation:

How to solve self-consistent equations?