At time t = 0 a particle is represented by the wave function \psi(x)=N \times\left\{\begin{array}{ll}

e^{x} & x<0 \\

\cos x & 0 \leq x \leq \pi / 2 \\

0 & x>\pi / 2

\end{array}\right. (a) Find the normalisation constant N assuming it to be real and positive. (b) Sketch the wave function. What is the probability of detecting the particle at x > 0? (c) Compute (p), (p²), and the standard deviation op.