Which of the following functions, when multiplied by a normalization constant, would be acceptable one-dimensional wave functions for a bound particle? (a and b are positive constants, and x goes from -∞ to ∞)
(a) e-ax;
(b) e-bx2;
(c) xe-bx2;
(d) ie-bx2;
(e) f(x) = e-bx2 for x < 0, f(x) = 2e-bx2 for x ≥ 0.