## What is a well-behaved function in quantum mechanics?

Answer: Well behaved wave function is the wave function which is single valued, continuous and finite. Explanation: Well behaved wave function is the wave function which is single valued, continuous and finite. It must be single valued to get good probability.

## Which of the following are 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 the wave function ψ represent?

Wave Functions. A wave function (Ψ) is a mathematical function that relates the location of an electron at a given point in space (identified by x, y, and z coordinates) to the amplitude of its wave, which corresponds to its energy.

### Why should the wave function be single valued everywhere?

The wave function must be single valued. This means that for any given values of x and t , Ψ(x,t) must have a unique value. This is a way of guaranteeing that there is only a single value for the probability of the system being in a given state.

### What makes a valid wavefunction?

These aspects mean that the valid wavefunction must be one-to-one, it cannot have an undefined slope, and cannot go to −∞ or +∞. For example, the wavefunction must not be infinite over any finite region.

Why should wave function be single valued?

#### Can wave function be constant?

Yes exactly. The particle on a ring has a constant wavefunction for the k=0 momentum eigenstate. The s-orbital in an atom is a bit like a constant wave function too, except it decays with radius.

#### Is Heisenberg uncertainty principle?

uncertainty principle, also called Heisenberg uncertainty principle or indeterminacy principle, statement, articulated (1927) by the German physicist Werner Heisenberg, that the position and the velocity of an object cannot both be measured exactly, at the same time, even in theory.

What is the significance of ψ and ψ 2?

ψ is a wave function and refers to the amplitude of electron wave i.e. probability amplitude. It has got no physical significance. The wave function ψ may be positive, negative or imaginary. [ψ]2 is known as probability density and determines the probability of finding an electron at a point within the atom.

## What are acceptable wave functions?

The wave functions must form an orthonormal set. This means that • the wave functions must be normalized. The wave function must be finite everywhere. 6. The wave function must satisfy the boundary conditions of the quantum mechanical system it represents.