How many points of zero probability in a finite well?

In summary, in a finite potential well deep enough to allow for an electron state with n=4, there are (a) n-1 points of zero probability and (b) n points of maximum probability for its matter wave. The analogy between clamped strings and quantization fails in this case, as the wavefunction probability is non-zero in the potential. The number of nodes is n+1 and the number of antinodes is n.
  • #1
L_landau
27
0

Homework Statement


An electron is trapped in a finite potential well that is deep enough to allow the electron to exist in a state with n=4. How many points of (a) zero probability and (b) maximum probability does its matter wave have within the well?

Homework Equations


For infinite potential well there are nodes at the walls and λ = 2L/n as in the case of a string with two clamps.
In this case there are n+1 nodes and n antinodes.

The Attempt at a Solution


I read in the textbook that the analogy between clamped strings and quantization fails for the finite potential well because the wavefunction probability is non-zero in the potential. Judging by the graphic included, I would say that there are (a) n-1 nodes and (b) n antinodes for the finite potential well case. Is this right?
 

Attachments

  • Screen Shot 2017-10-01 at 11.42.23 AM.png
    Screen Shot 2017-10-01 at 11.42.23 AM.png
    12.3 KB · Views: 523
Physics news on Phys.org
  • #2
L_landau said:
Judging by the graphic included, I would say that there are (a) n-1 nodes and (b) n antinodes for the finite potential well case. Is this right?
Yes, that's right.
 

FAQ: How many points of zero probability in a finite well?

How do you define a finite well?

A finite well is a quantum mechanical potential energy barrier that has a finite width and depth. It is often used to model the confinement of particles in a specific region.

What are the points of zero probability in a finite well?

The points of zero probability in a finite well are the locations where the wave function of a particle is equal to zero. These points are typically found at the boundaries and at the center of the well.

How many points of zero probability are there in a finite well?

The number of points of zero probability in a finite well depends on the specific dimensions and shape of the well. In general, there can be multiple points of zero probability, but the exact number can vary.

What is the significance of the points of zero probability in a finite well?

The points of zero probability in a finite well represent the locations where the particle has no chance of being found. This is due to the wave function being equal to zero at these points, indicating that the particle cannot exist there.

How do the points of zero probability affect the behavior of particles in a finite well?

The points of zero probability play a crucial role in determining the energy levels and allowed states of particles in a finite well. They also influence the probability of tunneling through the well barrier. Understanding the points of zero probability is essential in studying the behavior of particles in a finite well.

Similar threads

Finite quantum well, multiple choice question
Replies
3
Views
1K
Electron in a Finite Square Well
Replies
1
Views
1K
Help Calculating probability between 2 limits for the ground state
Replies
28
Views
1K
Is My Quantum Well Probability Calculation Correct?
Replies
9
Views
1K
What Are the Correct Values for Probability and Momentum in a Quantum Well?
Replies
1
Views
861
What Do Coefficients and Expectation Values Mean in Quantum Mechanics?
Replies
8
Views
3K
Calculating Amplitude of Standing Wave at a Given Point
Replies
1
Views
2K
Finite/Infinite Potential Well Problems
Replies
4
Views
5K
How Small Can a Quantum Well Be for an Electron's Total Energy to Be Zero?
Replies
4
Views
2K
Standing Waves: Synchronization between a Tube & a Stick
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top