Infinite square well

Please I'm new here, and would need your help with identifying what sort of potential function is described by the following expression:

V(x) = 0 for |x| < 1, =1 at x = \pm 1, and =\infty for |x|>1.

(Note that: \pm is plus (+) or minus (-) sign).

Could it be referred to as the infinite well potential? If not, what kind of potential can it be called, and where can it be applied.

I'm particular interested in solving the 1-D Schrodinger time-independent equation:

H_{0}f(x) + V(x)f(x)= E f(x),

where H_{0} is the usual Laplace operator

Thank you!