Kronig-Penney Model: Understanding Electron Potential Energy

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SUMMARY

The discussion centers on the Kronig-Penney model's treatment of electron potential energy, specifically the discrepancy between the potential energy values in Charles Kittel's textbook and the Wikipedia entry. Kittel describes the potential as positive (Vo) in his model, while the Wikipedia source indicates it as negative. This raises questions about the implications for the solutions of the Schrödinger equation in different regions of the potential. The participants assert that the difference in sign is merely a matter of adding or subtracting a constant energy, which does not fundamentally alter the physics of the problem.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly the Schrödinger equation.
  • Familiarity with potential energy concepts in quantum systems.
  • Knowledge of the Kronig-Penney model and its applications in solid-state physics.
  • Ability to interpret graphical representations of potential energy diagrams.
NEXT STEPS
  • Study the derivation of the Schrödinger equation solutions for the Kronig-Penney model.
  • Examine the implications of potential energy sign conventions in quantum mechanics.
  • Explore the differences between periodic potentials and their effects on electron behavior.
  • Review additional resources on the mathematical treatment of potential energy in quantum systems.
USEFUL FOR

Students and professionals in physics, particularly those focused on quantum mechanics and solid-state physics, will benefit from this discussion. It is especially relevant for those studying the behavior of electrons in periodic potentials and the implications of potential energy definitions.

manofphysics
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We know electron has potential energy as shown in fig 1 .
Now in my book ( Charles Kittel) it is written that kronig and penney modified this to be a square potential as shown in fig 2.
How is the potential in fig 2( inkronig penney model) drawn to be positive (Vo) if in figure 1 it is shown to be negative ( and rightly so,as in my opinion, potential energy of electron should be negative in presence of positive charge)?
Will the Schrödinger eqn solutions not change in the resp. regions if we arbitrarily change the sign of the potential energy to positive as has been done in kittel?
And one note: http://en.wikipedia.org/wiki/Partic...tice_(periodic_potential)#Kronig-Penney_model :here Vo is taken to be negative and hence Schrödinger eqn soln is different in -b<x<0 from the one given in Kittel.Is this and kittel both right?
Fig 1 and fig2 are attached
 

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  • fig 2.gif
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Man of physics, come on, that's just a point of adding or subtracting a constant energy!
 

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