Find Particle Given Wavefunction: Probability Amplitude & Exponential Decay

[stunner5000pt]

Homework Statement

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

Homework 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

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??

thanks for your help!

 

[OlderDan]

Homework Statement

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

Homework 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

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??

thanks for your help!

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