Schrodinger equation & Wave Mechanics

Consider a rectangular potential barrier $V(x) = V_0$ for $a < x < b$ and 0 elsewhere, with $V_0 > 0$. For particles of energy $E < V_0$ incident on this barrier from the left ($x < a$), which schematic diagram best represents the probability density $|\psi(x)|^2$ as a function of $x$?

Options:

• (A) Oscillatory in $x < a$, exponentially decaying in $a < x < b$, and oscillatory with reduced constant amplitude in $x > b$
• (B) Oscillatory in $x < a$, growing exponentially in $a < x < b$, and zero in $x > b$
• (C) Constant everywhere
• (D) Zero everywhere inside the barrier