Probability density Definition and 273 Threads

I find quantum mechanics to be very hard, and I am currently having trobule with the following 2 problems, can someone please help me out? 1) A thin solid barrier in the xy-plane has a 10-micrometer-diameter circular hole. An electron traveling in the z-direction with vx=0 m/s passes...

So the integral of |Psi| squared represents the probability of finding a particle at a certain position at a certain time. Please correct me if this is wrong. SO what exactly does the "density" refer to?

Homework Statement Let X and Y be random variables. The pdfs are f_X(x)=2(1-x) and f_Y(y) = 2(1-y). Both distributions are defined on [0,1]. Let Z = X + Y. Find the pdf for Z, f_Z(z). Homework Equations I'm using ideas, not equations. The Attempt at a Solution I'm dying of...

Homework Statement This is my 1st post here, so I will do my best. The following question is part of a number of probability density functions that I have to prove. Once I have the hang of this I should be good for the rest, here is the question: Prove that the following functions are...

I was reading that moment generating functions have the property of uniqueness. So just wondering: is there a way to get a probability density function from a moment generating function?

[FONT="Comic Sans MS"] we often say that the square of wave function gives us the probability density where the particle is. how can the square of a function might predict about the existence of a particle?

Probability Density Function...Help The probabiltiy density function of the time to failure of an electric component in hours is f(x)=e^{(-x/3000)/3000} for x > 0 and f(x) = 0 for x \leq 0 determine the probability that a) A component last more than 1000 hours before failure I know how...

Not really a homework question, but a problem I don't get nonetheless. The density of fragments lying x kilometers from the center of a volcanic eruption is given by: D(r) = 1/[sqrt(x) +2] fragments per square kilometer. To 3 decimal places, how many fragments will be found within 10...

Quick question: I just started reading Feynman's Lectures and in one section (6-4) he says that for a system in which a particle (in 1 dimension) can move in either direction (with equal prob. of either direction). For each 'step' that the particle takes, the distance it moves can be any...

Probability Density Function -- Need Help! Hi, Can someone please check my work if i did the problem correctly? thanks in advance. Here is the problem: Find the PDF of W = X + Y when X and Y have the joint PDF fx,y (x,y) = 2 for 0<=x<=y<=1, and 0 otherwise. here is my solution...

I have a problem where there are two resistors in parallel and I need to find the equivalent resistance. R1 = X and R2 = Y, and X and Y are independent random variables, uniform over the range of 100-120. If R equivalent = Z = XY/X+Y, what is probability density function of Z?

I have a problem where there are two resistors in parallel and I need to find the equivalent resistance. R1 = X and R2 = Y, and X and Y are independent random variables, uniform over the range of 100-120. If R equivalent = Z = XY/X+Y, what is probability density function of Z?

Hi Guys, I am having some trouble trying to solve a probability density function question. ...If the density function is: f(x) = 9x^3, 0 < x 1. What is the conditional probability of P(X > 0.2 | X <0.6) ?? Any help would be greatly appreciated :)

Here's the question: The needle on a broken car spedometer is free to swing, and bounces perfectly off the pins at either end, so that if you give it a flick it is equally likely to come to rest at any angle between 0 and \pi . Consider the x-coordinate of the needle point - that is, the...

Have known a wave function, how get does distributing density function of the probability?

Will P(r) depend on time? Explain your reasoning. The wavefunction is \frac{1}{\sqrt{2}} (\psi_{2,1,-1}+\psi_{2,1,1}) \frac{1}{16}\,{\frac {r{e^{-1/2\,ra}}\sin \left( \theta \right) \left( {e^{-i \phi}}-{e^{i\phi}} \right) \sqrt {2}\sqrt {{\pi }^{-1}}}{\sqrt {{a}^{3 }}a}}...

I realize that electron probability density is the probability of finding an electron in a given volume, but as I was working on some homework, I wasn't sure how this fact would apply. Under what circumstances is an atomic electron's probability-density distribution spherically symmetric?

I realize that electron probability density is the probability of finding an electron in a given volume, but as I was working on some homework, I wasn't sure how this fact would apply. Under what circumstances is an atomic electron's probability-density distribution spherically symmetric? Why...

Suppose that X and Y are independent random variables, where X is normally distributed with mean 45 and standard deviation 0.5 and Y is normally distributed with mean 20 and standard deviation 0.1. (a) Find \ P(40 \leq X \leq 50, \ 20 \leq Y \leq 25). Ans. ~0.5 (b) Find \...

Consider the wave function corresponding to a free particle in one dimension. Construct the probability density and graph it as a function of position. Is this wavefunction normalizable? Now, I think that the function should be Psi = C1*exp(ikx-iEt). Thus, the probability density should be...

I want to "show that the classical probability density describing a particle in an infinite square well of dimension L is P(x) = 1/L." I know that classically, the particle bounces back and forth with constant kinetic energy and at constant speed, so at any given time it is equally likely to...

If the values of the joint probability density of Y1 and Y2 are as shown: 0 1 2 total 0 1/12 1/6 1/24 35/120 1 1/4 1/4 1/40 63/120 2 1/8 1/20 ... 21/120 3 1/120 ... ... 1/20 ttl 56/120 56/120 8/120 1 whew ;-) ok Find a) P (Y1=0) b) P(Y2=1 | Y1=1) c P(Y2=1) e Check if Y1...

For the ground state of the hydrogen atom, evaluate the probabilty density psi^2(r) and the radial probability density of P(r) for the positions. a) r = 0 b) r = rb I confused how this probability function is used. What's the technique here? Thanks