What Happens When a Spherical Square Well Approaches 2mc2?

Click For Summary
SUMMARY

This discussion focuses on the behavior of a Dirac particle in an attractive spherical square well as the potential depth approaches 2mc². The participant has solved the transcendental equation for energy and normalized the wave function but is struggling to derive significant insights when V0 equals 2mc². They reference Greiner's work, specifically Eq.(27) on page 220, and seek assistance in obtaining values from table 9.2 on page 222 related to V0(κ=-1). The participant is looking for alternative consequences of the well depth approaching this critical value.

PREREQUISITES
  • Understanding of Dirac particles and their wave functions
  • Familiarity with spherical square well potentials
  • Knowledge of transcendental equations in quantum mechanics
  • Ability to interpret and manipulate equations from quantum mechanics literature, specifically Greiner's textbook
NEXT STEPS
  • Research the implications of potential depth in quantum mechanics, focusing on V0 ≥ 2mc²
  • Study the derivation and significance of Eq.(27) in Greiner's text
  • Examine the consequences of well depth on particle behavior in quantum wells
  • Explore methods to extract values from tables in quantum mechanics literature, particularly in the context of spherical potentials
USEFUL FOR

Students and researchers in quantum mechanics, particularly those studying Dirac particles and potential wells, as well as educators looking for insights into advanced quantum topics.

sean_mp
Messages
18
Reaction score
0

Homework Statement


I'm dealing with a dirac particle in an attractive spherical square well. I've solved for the transcendental equation to find energy, found the normalized wave function, and now I'm trying to explain what happens when the well becomes very deep, when V0 ≥ 2mc2. If I plug V0=2mc2 into my equations, nothing dramatic really sticks out. I have the same equation as Greiner on page 220, Eq.(27).

Homework Equations


I'm trying to get the values in the left hand side of table 9.2 on page 222 (V0(κ=-1)), but I'm not sure how to go about it. If I can't solve for this, I need to come up with another consequence of the well depth approaching 2mc2.

The Attempt at a Solution

 

Attachments

Last edited by a moderator:
Physics news on Phys.org
I've tried plugging in V0=2mc2 into Eq.(27), but this doesn't really seem to get me anywhere. I'm not sure what else to do. Any help would be greatly appreciated!
 

Similar threads

What is the Depth of the Potential Well for an Odd Bound State Solution?
  • · Replies 2 ·
Replies
2
Views
4K
Bound state of a square well, no allowed bound state mean?
  • · Replies 7 ·
Replies
7
Views
3K
Finding range of bound/non bound state energies of 1D finite
  • · Replies 3 ·
Replies
3
Views
2K
Bound state of 3-dimensional Dirac well
  • · Replies 12 ·
Replies
12
Views
2K
What Is the Probability of Particle Ionization in a Shifted Finite Square Well?
  • · Replies 4 ·
Replies
4
Views
2K
Explore Formation of Bound State in a Delta-Function Potential Well
  • · Replies 8 ·
Replies
8
Views
8K
Find Energies Bound States Potential Well: Time Independent SE
  • · Replies 4 ·
Replies
4
Views
2K
Possible bound states of a one-dimensional square well I'm Lost
  • · Replies 1 ·
Replies
1
Views
2K
Instantaneous doubling of the Infinite Square Well Width
  • · Replies 1 ·
Replies
1
Views
4K
Infinite Square well with a Finite square well inside
  • · Replies 7 ·
Replies
7
Views
5K