# Schrodinger Equations and Probability Density Functions

## Homework Statement

A Particle is described by the normalized wave function
psi(x,y,z) = Ae^(-alpha[x^2 + y^2 + z^2])
Where A and alpha are real positive constants

a)Determine the probability of finding the particle at a distance between r and r+dr from the origin
hint: use the volume of the spherical shell centered on the origin with inner radius r and thickness dr.
b) For what value of r does the probability in part a) have it's maximum value? Is this the same value of r for which |psi(x,y,z)|^2 is a maximum? explain any differences

|psi(x)|^2 = 1

## The Attempt at a Solution

Got no idea, like all 4 questions i'm posting any help would be appreciated, as i am completely lost

## Answers and Replies

malawi_glenn
Science Advisor
Homework Helper
the integration measure for sphere is r^2dr d(phi) d(cos theta)

for a) just use the hint, take the probability of finding particle inside sphere with radius r + dr and substract with the probabilitiy to find it inside sphere with radius r.

for b) you know how to find maxima of a given function right?