Question

A quantum particle has a wave function $$ \psi(x)=\left\{\begin{array}{ll} \sqrt{\frac{2}{a}} e^{-x / a} & \text { for } x>0 \\ 0 & \text { for } x<0 \end{array}\right\} $$ (a) Find and sketch the probability density. (b) Find the probability that the particle will be at any point where $x<0 .$ (c) Show that $\psi$ is normalized and then find the probability of finding the particle between $x=0$ and $x=a$

          A quantum particle has a wave function
$$
\psi(x)=\left\{\begin{array}{ll}
\sqrt{\frac{2}{a}} e^{-x / a} & \text { for } x>0 \\
0 & \text { for } x<0
\end{array}\right\}
$$
(a) Find and sketch the probability density. (b) Find the probability that the particle will be at any point where $x<0 .$ (c) Show that $\psi$ is normalized and then find the probability of finding the particle between $x=0$ and $x=a$

Added by Erik H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Andrew Sullivan

07/07/2022

Step 1

Step 1: The probability density function is given by $p(x) = 2/a \cdot e^{-2x/a}$. Show more…

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A quantum particle has a wave function $$ \psi(x)=\left\{\begin{array}{ll} \sqrt{\frac{2}{a}} e^{-x / a} & \text { for } x>0 \\ 0 & \text { for } x<0 \end{array}\right\} $$ (a) Find and sketch the probability density. (b) Find the probability that the particle will be at any point where $x<0 .$ (c) Show that $\psi$ is normalized and then find the probability of finding the particle between $x=0$ and $x=a$