# Find the particle

1. Dec 11, 2006

### stunner5000pt

1. The problem statement, all variables and given/known data
Where is the particle most likely to be found given the wavefunction in the diagram
Also the wavefunction decays exponentially as x goes to infinty

2. Relevant equations
well the wavefunction is the probability amplitude
the square modulus of the wavefunction gives the probability desnity
and the square modulus times delta x gives the probability of finidng a particle bewtween x and x + delta x

3. The attempt at a solution
i think it is most likely to be fond where the probability amplitude is maximum because at those regions the particle has maximum proabiltiy of being found

is this correct??

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2. Dec 11, 2006

### OlderDan

Yes

In 3-D you do have to be careful with radial wave funcions. The usual thing is to plot rR(r) because R(r) itself is not sufficient to find the most likely r. That's bcause a particle can be found at one value of r and be anywhere in a shell of radius r and thickness dr. The volume of the shell increases in proportion to the area of a sphere, or as r²