# Can this function be a wavefunction of a physical system?

Gold Member

## Homework Statement

Can this function be a wavefunction of a physical system with finite potention energy:
$$\psi(x)=\frac{A}{\sqrt{x^2+b^2}}$$

no

## The Attempt at a Solution

The ans is YES.
1)it is continuous.
2)its derivative also continous.
3)It can be normalized, as it tends to zero as x tends to infinity. Also when x=0, this function is finite.

Is the above argument enough? Also for 3), do i need to do an integration to prove it can be normalized? Thanks!