Probability of finding particle

  • Context: Graduate 
  • Thread starter Thread starter Aziza
  • Start date Start date
  • Tags Tags
    Particle Probability
Click For Summary

Discussion Overview

The discussion revolves around the probability of finding a particle described by a specific wavefunction, ψ(x,0) = \frac{1}{\sqrt{a}}exp^(-|x|/a). Participants explore the implications of this wavefunction on the probability of locating the particle within a defined range, particularly addressing the independence of this probability from the variable x0.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the validity of the wavefunction due to a perceived sharp point at x=0, suggesting that wavefunctions should not have sharp bends.
  • Multiple participants assert that the probability is not independent of x0, prompting inquiries about the role of the constant 'a' in the wavefunction.
  • Another participant emphasizes that 'a' is not merely a constant but has significant implications, hinting at its dimensions and relationship to the wavefunction's behavior.
  • A later reply suggests a connection between 'a' and the maximum height of the probability curve, proposing that as x0 increases, the maximum height decreases, which may keep the probability constant over the interval.
  • There is a clarification that 'a' and x0 are considered equivalent in the context of the book, which may affect the interpretation of the problem.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the probability is independent of x0, with some arguing for independence and others against it. The discussion remains unresolved regarding the implications of the wavefunction and the role of the constant 'a'.

Contextual Notes

The discussion highlights potential limitations in understanding the wavefunction's properties, particularly regarding the assumptions about continuity and the implications of the constant 'a'.

Aziza
Messages
189
Reaction score
1
This is example from my book:

For some particle, let ψ(x,0) = [itex]\frac{1}{\sqrt{a}}[/itex]exp^(-|x|/a).

Finding the probability that the particle is found between -x0 and x0 yields a probability of 86.5%, independent of x0! But how can this be, since as x0 tends to infinity, the probability of finding the particle between negative infinity and infinity must be 1...so the probability suddenly jumps from 86% to 100%?

I am thinking that maybe this is not a valid wavefunction since it has a sharp point at x=0 and my professor said that the wavefunction cannot have any sharp bends...?
 
Physics news on Phys.org
It's not independent of x0. What is the role of a here?
 
Vanadium 50 said:
It's not independent of x0. What is the role of a here?

It is just a constant, sorry I forgot to mention that.
 
It's not just a constant. It plays a very important role. What is it?

Hint: what are its dimensions?

Note also that your original problem doesn't specify that x0 is a special value of x.
 
Vanadium 50 said:
It's not just a constant. It plays a very important role. What is it?

Hint: what are its dimensions?

Note also that your original problem doesn't specify that x0 is a special value of x.

ohhh i think i see...a is related to the max height of the curve which is itself related to x0 so as x0 increases the max height decreases, thus keeping the probability constant in that interval...right?
 
What you're calling 'a' is called x0 in the book. 'a' and x0 are exactly the same thing.
 

Similar threads

Undergrad 100 boxes of Length L, an application of the famous Particle in A Box
  • · Replies 11 ·
Replies
11
Views
2K
Undergrad Probability of finding a particle outside its light cone
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad How to get the wavefunction of a single particle in QFT?
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Concept of wavefunction and particle within Quantum Field Theory
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Quantum Zeno effect to influence a particle's movement
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Probability of Staying in x<0 for Superposition of 2 Gaussians
  • · Replies 10 ·
Replies
10
Views
2K
Graduate Probability of finding a particle [concept behind it]
  • · Replies 3 ·
Replies
3
Views
1K
Graduate Does Antony Valentini's "sub-quantum measurement" really work?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Transition probability and superposition
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Normalizing a wavefunction and probability help
  • · Replies 2 ·
Replies
2
Views
3K