A particle is trapped in an infinite one-dimensional well of width $L$. If the particle is in its ground state, evaluate the probability to find the particle $(a)$ between $x=0$ and $x=L / 3 ;(b)$ between $x=L / 3$ and $x=2 L / 3 ;(c)$ between $x=2 L / 3$ and $x=L$

Name: A particle is trapped in an infinite one-dimensional well of width L. If the particle is in its ground state, evaluate the probability to find the particle (a) between x=0 and x=L / 3 ;(b) between x=L / 3 and x=2 L / 3 ;(c) between x=2 L / 3 and x=L
Uploaded: 2021-06-29T01:02:30-08:00
Duration: 7 min 22 s
Channel: Mehdi Hatefipour
Description: A particle is trapped in an infinite one-dimensional well of width L. If the particle is in its ground state, evaluate the probability to find the particle (a) between x=0 and x=L / 3 ;(b) between x=L / 3 and x=2 L / 3 ;(c) between x=2 L / 3 and x=L

          A particle is trapped in an infinite one-dimensional well of width $L$. If the particle is in its ground state, evaluate the probability to find the particle $(a)$ between $x=0$ and $x=L / 3 ;(b)$ between $x=L / 3$ and $x=2 L / 3 ;(c)$ between $x=2 L / 3$ and $x=L$

Added by Darrell F.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Mehdi Hatefipour

06/29/2021

Step 1

Step 1: The probability of finding the particle between $x=0$ and $x=L/3$ is given by the integral of the probability density function $\psi^2(x)$ from $0$ to $L/3$: \[ P(0 \leq x \leq L/3) = \int_{0}^{L/3} \psi^2(x) dx = \frac{2}{L} \int_{0}^{L/3} Show more…

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A particle is trapped in an infinite one-dimensional well of width $L$. If the particle is in its ground state, evaluate the probability to find the particle $(a)$ between $x=0$ and $x=L / 3 ;(b)$ between $x=L / 3$ and $x=2 L / 3 ;(c)$ between $x=2 L / 3$ and $x=L$