Probability density Definition and 273 Threads

Hi, I am trying to figure out the following integral. I have two normalized 1D harmonic osccilator wave functions \psi_{n}(x) and \psi_{m}(x) and I would like to integrate \int_{\text{all space}} |\psi_{n}(x)|^2 |\psi_{m}(x)|^2 dx for m\neq n . I would also be interested in knowing...

Hi, I have a probability density function defined by 1 / D x E . eABC/2 D is a single number E is a determinant of a matrix . is the dot product between the two sides of the function e I am pretty sure is meant to be eulers constant A is a 5x1 vector B is a 5 x 5 matrix C is a...

Hi, I have a probability density function defined by 1 / D x E . eABC/2 D is a single number E is a determinant of a matrix . is the dot product between the two sides of the function e I am pretty sure is meant to be eulers constant A is a 5x1 vector B is a 5 x 5 matrix C is...

In the book Introduction to Quantum Optics: From the Semi-classical Approach to Quantized Light by Grynberg, Aspect and Fabre I came across the following statement on page 385: "By the end of the nineteenth century, classical electromagnetism,..., provided a wave description of almost all...

Homework Statement The Attempt at a Solution I think I'm just evaluating integrals in this problem, not so? For part a) \int_0 ^1 λe^{-λt}dt = \int_0 ^1 e^{-t}dt = -e^{-t} |^1 _0 = \frac{-1}{e} + 1 For part b) \int_0 ^3 e^{-t}dt = -e^{-t} |^3 _0 = \frac{-1}{e^3} + 1 For part c) \int_3 ^4...

The phones offered by a cell phone company have some chance of failure after they are activated. Suppose that the density function p(t) describing the time t in years that one of their phones will fail is p(t) = 1-e^{-λt} for t ≥ 0, and 0 otherwise. The cell phone company offers its clients a...

This might not be in the right place but here it goes: Homework Statement A given periodic function in time is given u(t). I must compute the probability density function that describes u. u(t) = A sin (2π / T t + ψ) A and ψ are constants. T is the period. t is time. Homework EquationsThe...

Homework Statement Suppose X selects an integer from the set S = {0,1,...,9} and Y selects an integer from {0,...,x^2}. Find: (a) f(x,y) [joint prob density func] (b) fY(y) [marginal for Y] (c) Probability (Y <= 10 | X = 5) (d) Probability (Y <= 10 | X <= 5)Homework Equations The Attempt at a...

Homework Statement F(x)=k(1-1/x2), 1\leqx<2 Homework Equations The Attempt at a Solution How do I get the probability density function here? Simply take the derivative of this function ? 1\int2 = k(1-1/x2) Supposed to be 1 at the bottom and two at the top.

/// The probability density does not go to zero at the nodes if relativistic effects are taken into account. /// src=wikipedia, particle in a box. /// so does it mean energy levels/atomic orbitals are not necessarily discrete and that atom has to be remodeled. ***pardon my ignorance if I...

why the probability density doesn't oscillate with time?

Homework Statement Let f(x,y)=xe^{-xy} x \geq 0, y \geq 1 is this a probability density function? If not, find a constant that makes it a pdf. Homework Equations To be a pdf, we must have \int_1^\infty \int_0^\infty \! xe^{-xy} \, \mathrm{d} x \mathrm{d} y=1 The Attempt at a...

In QM people always talk about probability amplitudes and probability densities, but I've never really given these terms much thought and have always just ignored the density/amplitude part and focussed on the probability part. So what is meant by a probability density - is it what it sounds...

Homework Statement Random voltage is defined with its probability density function: p_{\xi}(v)=2,25u(v+2)e^{-3(v+2)}+k\delta (v-2) u-Heaviside step function a) Find constant k. b) What is the probability of a random variable to take value of 2. c) Find the cumulative distribution function...

Hello, I'm somewhat confused by the expression f(X = x | Y = y) = \frac{f(X=x)}{f(Y=y)} (which, if I'm right, is the definition of a conditional probability density? My course seems to state it as a theorem, without proof, but then again my course is a little bit vague; although I welcome...

Hello everyone! I am stuck in my research with a probability density function problem.. I have 'Alpha' which is a random variable from 0-180. Alpha has a uniform pdf equal to 1/180. Now, 'Phi' is a function of 'Alpha' and the relation is given by, Phi = (-0.000001274370471*Alpha^4) +...

Homework Statement In a neutral hydrogen atom, the electronic ground state 1s, and excited state 2s, are given by wave functions ψ1s = 1/π1/2 1/a3/2 e-r/a ψ2s = 1/(32π)1/2 (2-r/a)2 e-r/(2a) where "r" is the radial distance to the nucleus, and "a" is the Bohr radius. Write a C++ program...

Homework Statement A C O2 molecule is released at the center of a closed room where the air is perfectly still. Take the center as the origin of coordinates. After time t has elapsed, the position of the molecule r is uncertain, but is described by the probability distribution function...

I have a 3 dimensional orbital-specfic electron density function ( |\psi(r)|2 ) for all relevant r values. How would I go about finding the corresponding \psi(r)? I know it would be something related to a Fourier transform, I'm just unsure about how to go about performing it in mathematica or...

My goal here is to at least approximately calculate the probability density function (PDF) given the moment generating function (MGF), M_X(t). I have managed to calculate the exact form of the MGF as an infinite series in t. In principle, if I replace t with it and perform an inverse...

Hello! I have been having problems with understanding how the probability density function is calculated. However, at the same time, I need it urgently for my research. Well, you could start by giving me a definition of 1. Refernce measure 2. That 'E' sign(looks like an epsilon, and I sound...

hey guys, i am really confused on something.here is the thing: i have; i=x+(x^2-y)^(1/2) and here x is uniform distribution on (a,b) y is uniform distribution on (c,d) x and y independent i need to find the probability density function of i but how? actually i don't know how to...

I have looked around for an answer to this. People just call it a "rule". So is it just assumed that the wavefunction of a particle times its complex conjugate is a probability density, or is there some way to show this? For instance, why isn't probability density equal to |wavefunction|^4 or...

Homework Statement The random variable X has the probability density f(x) defined by: f(x) = ke(-|x|) Compute the constant k, then find the probability density of Y=X2 Homework Equations The Attempt at a Solution I'm completely stumped by this question. I know I need to...

Homework Statement I'm talking about the probability density plot of the harmonic oscillator. Is there some physical meaning to be extracted from this? Here's a link that contains the drawing of what I'm talking about http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc5.html...

Homework Statement Is the PDF of something between two different bases or wavefunctions always 0? For instance, if you have the lowering operator \hat{}a - <n|\hat{}a|n> that changes to <n|\sqrt{}n|n-1> =0 I'm not sure I understand the physical scenario if this is true however.

hi...does anybody know here...how you can calculate the probability density of photons?

Hello, given a continuous random variable x with a known PDF, how can we determine in general the PDF of the transformed variable f(x) ? For example f(x)=x+1, of f(x)=x2 ... ? Also, if we have two random variables x,y and their PDF's, is it always impossible to determine the PDF of f(x,y)...

The probability density for bullet hitting a target is given by f(x,y)=C.Exp(-(x^2+y^2)/2sigma square. What is the value of C. Sketch the curves of constant density in the XY plane. What kind of curve are they? What are the most probable hitting areas?

Homework Statement X and Y are random variables with the joint density: fXY(x,y) = k*e^(-lambda * x) if 0 < y < x < infinity = 0, otherwise Find P(X + 2*Y <= 3) Homework Equations I found k = lambda^2 The Attempt at a Solution I'm not sure exactly how to solve this, but...

normally distributed random variable with mean m and variance σ2. Find the PDF of Y

Continuous random variable X is defined in the interval 0 to 4, with P(X>x)= 1- ax , 0<=x<=3 = b - 1/2 x , 3<x<=4 with a and b as constants. Find a and b. So the area under the pdf is 1, then i integrated both functions and set up my first equation. Next, it seems that the...

Homework Statement c. The life of a certain brand of battery is normally distributed with a mean of 4 years and a standard deviation of 1. 2 years. i. If a battery is selected at random, what is the probability that it will last for more than 6 years? (5 marks) ii. How long a warranty...

This could go in the homework section I suppose, but I couldn't follow the guidelines, so I'll try asking it here. The attached image is a probability distribution for measured fibre angles from a spray up carbon fibre process. This is in a report that I need to explain. To get the...

Homework Statement So I understand how to evaluate P(4 < X < 6) where the probability density function is f(x)=4x I can't seem to understand how to evaluate P(X>6) I would have to do something like \int^6_\infty 4x ... so how do I evaluate it? Homework Equations The Attempt at a Solution The...

Homework Statement X,Y,Z random variables. Let Y and Z be two independent continuous random variables with common probability density function f(x) =2exp(-2x); x > 0 0; x < 0 (i) Specify the joint probability density function of (Y;Z). (ii) Fix x > 0. Let h(y; z) = 1...

Okay, this is a really basic question. I'm just learning the basics of QM now. I can't wrap my head around the idea that the radial distribution function goes to zero as r-->0 but that the probability density as at a maximum as r-->zero. How can this be? Thanks!

Homework Statement A point Q is chosen at random inside the unit square. What is the density function of the sum of the coordinates of point Q? What is the density function of the product of the coordinates of the point Q? Use geometry to find these densities. Homework Equations P(a <...

Homework Statement Let X be a posative random variable with probability density function f(x). Define the random variable Y by Y = X^2. What is the probability density function of Y? Also, find the density function of the random variable W = V^2 if V is a number chosen at random from the...

In my notes for a module on atomic and molecular physics it has this statement: "For a given n the probability density of finding e- near the nucleus decreases as l increases, because the centrifugal barrier pushes the e- out. So the low-l orbitals are called penetrating." I just want to...

Homework Statement a.) A lamp has two bulbs of a type with an average lifetime of 1000 hours. Assuming that we can model the probability of failure of these bulbs by an exponential density function with mean u = 1000, find the probablity that both of the lamp's bulbs fail within 1000 hours...

Homework Statement Xavier and Yolanda both have classes that end at noon and they agree to meet every day after class. They arrive at a campus cafe independently. Xavier’s arrival time is X and Yolanda’s arrival time is Y , where X and Y are measured in minutes after noon. The individual...

Homework Statement f(x)=&(x-a)exp((-(x-a)^2)/b) where a and b are constants Homework Equations find & in terms of b: show that the expected value of X is given by X=a + sqrt(pi*b/4) identity given x(x-a)=(x-a)^2+a(x-a) and integral from 0 to infinity of x^2*exp-x^2 dx=sqrt...

In a paper in Physical Review A, the author discusses a wave function for one particle, Ψ(r,t), where r is the position vector. He writes "The probability distribution for one-particle detection at a point r is given by [SIZE="4"]|<r|Ψ >|[SIZE="3"]2 ". Is that correct? The above...

Homework Statement the question asks you to calculate the standard derivation for the mean distance of an electron from the nucleus. you are given the mean distance (<r>), and the probability density Homework Equations delta r = sqrt (<r^2> - <r>^2) <r> = 3.a/2 The Attempt at a...

Homework Statement Roll a fair die three times Let X be the number of different faces shown all together ( X = 1,2,3 ) Find px(k) Homework Equations The Attempt at a Solution Alright so I kno that i need to get the individual probabilities of each outcome The first one where...

If an electron is in an infinite 1-D square well of width L, how do you get oscillation frequency of the probability density for any energy state n?

Hello I am trying to find the probability density function for a particle in a potential well of a harmonic oscillator. (My question is about complex conjugates). I know the formula. I have to multiply \Psi^{*} (x, t) \Psi (x, t)The wave function is a linear combination of stationary states...

Justification of ψ*ψdx as probability density of particle between x and x+dx using light's E-field and diffraction by slit. This isn't a homework problem, rather it was on the list of things to know for the exam. They don't really go over it in Griffiths Quantum Mechanics books. So are any...

Homework Statement Does a wavefunction have to be normalized before you can calculate the probability density? Homework Equations n/a The Attempt at a Solution Im thinking yes? so that your probability will be in between 0 and 1?