Quantum Mechanics solved problem-1

The energy eigenvalue and corresponding eigenfunction for a particle in one-dimensional potential $V(x)$ are:

$E=0, \quad \Psi(x)=\frac{A}{x^2+a^2}$

Where $A$ is a positive constant. The form of potential $V(x)$ is:

A. $\frac{\hbar^2(3x^2-a^2)}{m(x^2+a^2)^2}$

B. $\frac{\hbar^2(x^2-a^2)}{2m(x^2+a^2)^2}$

C. $\frac{\hbar^2(3x^2-a^2)}{m(x^2+a^2)^3}$

D. $\frac{\hbar^2(x^2-a^2)}{2m(x^2+a^2)^3}$

The correct Choice is A.

See the full solution from following video tutorial: