Wave function (schrodinger equation)

Click For Summary
SUMMARY

The discussion focuses on sketching the wave function ψ(x) for a particle with energy E in a potential well. Participants clarify that the wave function oscillates when E is greater than V0, while it decays exponentially when E is less than V0. Key points include the need for accurate amplitude and wavelength representation in different regions and the importance of understanding the behavior of the wave function in relation to potential barriers.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically wave functions.
  • Familiarity with the Schrödinger equation and its applications.
  • Knowledge of potential wells and energy levels in quantum systems.
  • Basic graphing skills to represent mathematical functions visually.
NEXT STEPS
  • Study the Schrödinger equation in one dimension for potential wells.
  • Learn about the concept of tunneling in quantum mechanics.
  • Explore graphical representations of wave functions in various potential scenarios.
  • Investigate the relationship between energy levels and wave function behavior in quantum systems.
USEFUL FOR

Students of quantum mechanics, physics educators, and anyone interested in understanding wave functions and potential wells in quantum systems.

asdf12312
Messages
198
Reaction score
1

Homework Statement


Sketch the wave function ψ(x) corresponding to a particle with energy E in the potential well shown below. Show correctly relative values of amplitude and wavelength in different regions.

wavefunc.png



Homework Equations


none?


The Attempt at a Solution


I guess I was a bit confused how to get started with this.. there's nothing like this in my notes so I'm kinda guessing. but from the picture I can see E is a staight line (constant) and it only oscillates when E>V0 otherwise it is decaying (e^x or something). So i graphed rough sketch of the wave function..am I doing anything that is wrong?
 
Physics news on Phys.org
Your understanding of what to do is correct. Of course in the region when the energy of the particle is greater than the potential: one measures a free particle like solution with varying frequencies.

There are two questionable parts for me in your solution. There isn't a decay before the first measurable wall and the second well oscillates too slowly being only 2 units higher than the first.
 

Similar threads

E<V Potential Step Confusion
  • · Replies 7 ·
Replies
7
Views
3K
Wave Function for a Particle in a Symmetric Infinite Square Well
  • · Replies 7 ·
Replies
7
Views
2K
Given the potential find the eigenfunction
  • · Replies 10 ·
Replies
10
Views
2K
Numerical Solution to Schrodinger Equation w/ Coulomb Potential
  • · Replies 1 ·
Replies
1
Views
2K
Solving a Piecewise Schrodinger equation
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Schrödinger equation and classical wave equation
  • · Replies 39 ·
2
Replies
39
Views
4K
Time dependent schrodinger equation and wave function
  • · Replies 3 ·
Replies
3
Views
2K
Time-independent Schrödinger equation, normalizing
  • · Replies 1 ·
Replies
1
Views
2K
Is the given wave function a stationary state?
  • · Replies 3 ·
Replies
3
Views
2K
Wave Functions With Same Energies Are the Same (only differ by a complex phase)
  • · Replies 5 ·
Replies
5
Views
2K