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 Quantum Physics Quantum Physics Help Forum May 21st 2019, 05:16 PM #1 Junior Member   Join Date: May 2019 Posts: 4 Probability graphs and reading them Given a probability over x graph, my questions were what is b in nm^-1 and what is the probability that you could find the particle between 20nm and 30nm. In attempts to this problem I tried to square the ψ(x) to get a probability density. I then assumed that under x the graph cancelled out what was about leaving me with 4b^2*10=1 and rearranging for b but this was incorrect and the actual answer was 0.0845 and I have no idea how they got to that answer. For the second part I realize that I have to intergrate the probability density in order to find the probability with an intergral of an upper limit of 30nm and lower limit of 20nm but I am also unsure of how exactly to intergrate the probability density   May 21st 2019, 07:18 PM #2 Forum Admin   Join Date: Apr 2008 Location: On the dance floor, baby! Posts: 2,811 The probability of the particle's position being between 20 and 30 nm is $\displaystyle P = \int _{20~nm}^{30~nm} \psi ^* (x) \psi (x)~dx$ as you say. Since everything is nice and real all we need to do is square the wavefunction. This gives $\displaystyle \psi ^* (x) \psi (x) = \begin{cases} 0 & 0 \leq x < 10 \\ 9b^2 & 10 \leq x < 20 \\ 4b^2 & 20 \leq x < 30 \\ b^2 & 30 \leq x < 40 \\ 0 & 40 \leq x \end{cases}$ So we have that $\displaystyle \int _{20} ^{30} \psi ^* (x) \psi (x)~dx = 4b^2 \cdot 10$ You didn't ask this so I'm assuming you know how to grok it: The total probability of the particle being anywhere is 1. So we know that $\displaystyle 140b^2 = 1$. Thus we normalize our $\displaystyle \psi (x)$ we get $\displaystyle \int _{20} ^{30}\psi ^* (x) \psi (x) ~dx \to \dfrac{4b^2 \cdot 10}{140b^2} = \dfrac{40}{140} = 0.286$ -Dan studiot and CBM like this. __________________ Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup. See the forum rules here.  Tags graphs, probability, reading Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post THERMO Spoken Here Thermodynamics and Fluid Mechanics 0 Jun 6th 2016 01:53 PM tadkins Advanced Thermodynamics 0 Sep 10th 2012 09:21 AM BIOS Waves and Sound 0 Jan 7th 2011 12:28 PM Sophia Kinematics and Dynamics 1 Feb 15th 2009 10:26 PM werehk General Physics 3 Jun 7th 2008 07:45 AM