Can this function be a wavefunction of a physical system?

[td21]

Homework Statement

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

Homework Equations

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!

 

[dextercioby]

Assuming the potential to be time independent, can it be a solution to the spectral equation of the Hamiltonian ?

for 3), you need to do the integration and show that A is finite.