Finding the probability of an electron

Click For Summary

Homework Help Overview

The discussion revolves around determining the probability of finding an electron in a specific region defined by the negative psi 320 wavefunction, particularly in a toroidal region. The subject area is quantum mechanics, focusing on wavefunctions and probability distributions.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of the roots of cos(theta) and their relation to the angular part of the wavefunction. Questions arise about the role of the radial part and whether it can be negative, as well as the nature of the wavefunction itself.

Discussion Status

The discussion is active, with participants questioning the relationship between the radial and angular components of the wavefunction. Some guidance has been offered regarding the positivity of probability and the need to examine the functional form of the wavefunction.

Contextual Notes

Participants note that the quantities discussed are squares of the relevant factors of the wavefunction and mention normalization concerns. There is an emphasis on the constraints that probability values must remain between 0 and 1.

apott155
Messages
4
Reaction score
0

Homework Statement



Determine the probability of finding the electron in the region for which the psi 320 wavefunction is negative(toroidal region).

Homework Equations





The Attempt at a Solution


cos (theta)=+/- sqrt 1/3

radial part integrated= r^6*e^(-2r/3a)

Angular part= (9cos(theta)^4-6cos(theta)^2+1)sin(theta)
 
Physics news on Phys.org
Can you use the roots cos (theta)=+/- sqrt 1/3 to determine a range of [tex]\theta[/tex] for which the angular part of the wavefunction is negative?
 
YUp.
 
I tried that, but I don't see where the radial part comes in
 
Can the radial part of the wavefunction ever be negative? Note that the quantities you wrote down are the squares of the relevant factors of the wavefunction. (they're also not normalized).
 
I don't think so... The ending value has to be inbetween 0 and 1 because its probability
 
apott155 said:
I don't think so... The ending value has to be inbetween 0 and 1 because its probability

Be careful. [tex]|\Psi|^2[/tex] is positive and bounded, but [tex]\Psi[/tex] itself isn't so restricted. In this case you need to examine the functional form.
 

Similar threads

Find the possible outcomes of ]##L^2## and ##L_{z}##
  • · Replies 21 ·
Replies
21
Views
3K
Discrepancies in Electron Wavefunction Probability Calculation?
  • · Replies 7 ·
Replies
7
Views
3K
Finding the probability of 1s electron within a cubical volume
  • · Replies 5 ·
Replies
5
Views
2K
Probability distribution of outgoing energy of particle
  • · Replies 1 ·
Replies
1
Views
3K
Probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##?
  • · Replies 1 ·
Replies
1
Views
2K
Spin probability of a particle state
  • · Replies 1 ·
Replies
1
Views
2K
Approximating Probability for a Wave Function
  • · Replies 2 ·
Replies
2
Views
2K
The increase of Fidelity after non-selective measurement
  • · Replies 1 ·
Replies
1
Views
2K
Some work on MTW Figure 25.7
  • · Replies 8 ·
Replies
8
Views
2K
Probability of finding a particle in the right half of a rectangular potential well
  • · Replies 16 ·
Replies
16
Views
3K