Ozenc Gungor, Teaching Assistant at Case Western Reserve University, Numerade Educator

11:21

Modern Physics

A particle is represented by the following wave function:
$$
\begin{array}{rlrl}
\psi(x) & =0 & x<-L / 2 \\
& =C(2 x / L+1) & & -L / 2<x<0 \\
& =C(-2 x / L+1) & & 0<x<+L / 2 \\
& =0 & & x>+L / 2
\end{array}
$$
(a) Use the normalization condition to find $C$. ( $b$ ) Evaluate the probability to find the particle in an interval of width $0.010 L$ at $x=L / 4$ (that is, between $x=0.245 L$ and $x=0.255 L$. (No integral is necessary for this calculation.)
(c) Evaluate the probability to find the particle between $x=0$ and $x=+L / 4$. ( $d$ ) Find the average value of $x$ and the rms value of $x: x_{\mathrm{rms}}=\sqrt{\left(x^{2}\right)_{\mathrm{av}}}$

Chapter 5: The Schrodinger Equation