What does it mean when a function is well-behaved?

A function which is continuous is “well behaved function”. For example if the value of the function can be estimated by looking to neighbouring values of the function then this function is called “well behaved one”.

What does well-behaved data mean?

For “well-behaved” data sets the empirical rule says that certain percentages of observations are within 1, 2, and 3 standard deviations of the mean. These percentages are (a) 65\%, 95\%, and 99\%. (b) 68\%, 90\%, and 99\% (c) 68\%, 95\%, and >99\%. (d) None of the above.

What are the characteristic of well-behaved wave function?

Characteristics a well-behaved wave function are: The function must be single-valued; i.e. at any point in space, the function must have only one numerical value.

What does well-behaved mean in mathematics?

In both pure and applied mathematics (e.g., optimization, numerical integration, mathematical physics), well-behaved also means not violating any assumptions needed to successfully apply whatever analysis is being discussed. The opposite case is usually labeled “pathological”.

What does well-behaved mean in the context of subroutines?

Ideally, additional axioms are introduced to ensure that a certain function (or any mathematical object, for that matter) is “well-behaved” which, in effect, makes analysis easier.

What are acceptable wave function?

The wave function must be square-integrable. In other words, the integral of |Ψ|2 over all space must be finite. A rapid change would mean that the derivative of the function was very large (either a very large positive or negative number). In the limit of a step function, this would imply an infinite derivative.

Which of the following conditions is incorrect for a well behaved wave function?

The condition (C) is incorrect. A well behaved wave function Ψ must be finite, single valued, continuous and should be zero at infinite distance.

Which of the following is not a characteristic of well behaved wave function?

Which of the following is not a characteristic of wave function? Explanation: The wave function has no physical significance.

What is a well-behaved vector field?

We usually deal with vector fields that are “well behaved”, i.e. no singularities (infinites), and no abrupt discontinuities (sudden jumps) no sudden breaks in direction. Examples: Velocities in a fluid, E-field, B-field.

Which of the following is not requirement of a well-behaved function?

Which of the following conditions is incorrect for a well behaved wave function (Ψ)?