- #1

Adoniram

- 94

- 6

## Homework Statement

A particle has a given wavefunction:

##ψ(x) = C e^{-x}(1-e^{-x})##

(many steps in between)

...

Find the most probable position of the particle

## Homework Equations

Most

*probable*is where the probability density's derivative = 0. Right?

##P(x) = |ψ(x)|^{2}##

## The Attempt at a Solution

I've solved for C, which 2√3.

Then I take the derivative of ##P(x)##, and set it to 0:

##-1-2e^{-2x}+3e^{-x}=0##

I've tried factoring this multiple ways and just can't seem to solve for x. I can do it in Mathematica no problem, but I could swear I've done this before and just can't remember the right tools.