Question: why cannot a particle in a infinitely deep potential well have zero energy

title: Particle in a box
text: i ħ ∂ ∂ t ψ ( x , t ) = − ħ 2 2 m ∂ 2 ∂ x 2 ψ ( x , t ) + V ( x ) ψ ( x , t ) , ( \ displaystyle i \ hbar ( \ frac ( \ partial ) ( \ partial t ) ) \ psi ( x , t ) = - ( \ frac ( \ hbar ^ ( 2 ) ) ( 2m ) ) ( \ frac ( \ partial ^ ( 2 ) ) ( \ partial x ^ ( 2 ) ) ) \ psi ( x , t ) + V ( x ) \ psi ( x , t ) , )