Question

Problem#2 please

B: What is the most likely outcome for d? C: What is the expectation value for d? D: Calculate (d2) and (d)2 E: Using your answers to C, calculate the standard deviation of d via Eq 1.12 in the book. F: Calculate Δd for each possible outcome. From these values, calculate the standard deviation via Eq. in the book. (This should be the same as D). 2 Gaussian probability distributions Consider the following probability density: ρ(x)-Ce-(z-zo) where ro and a are positive and real. A: Sketch p(x). Label how it depends on zo and a. B: For this to be properly normalized, what is C? Hint: look at the inside back cover of your book. Or another reference or software package (please let me know what you use so that I'm not mystified as to how you got your answer). C: Calculate (2) and Oz. 3 Choose your own wavefunction A: Write down a 1-D wavefunction that has the following properties: . It is properly normalized . There is zero probability of finding the particle anywhere outside the region between 0 Hints:

Answer 1

2)

a)

This is gaussian distribution

${\displaystyle f(x\mid \mu ,\sigma ^{2})={\frac {1}{\sqrt {2\pi \sigma ^{2}}}}e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}}$

comparing distribution

$C ={\frac {1}{\sqrt {\pi a ^{2}}}}$

c)

mean = $x_0$

$\sigma_x = \sqrt{\frac{a^2}{2}}$