How Does an Electric Field Affect Energy Levels in a Quantum Well?

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    Quantum Stark effect
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Discussion Overview

The discussion centers on the effects of an electric field on energy levels in a quantum well, specifically exploring methods to calculate shifts in subband energies. Participants are considering various theoretical approaches, including perturbation theory and variational methods, in the context of both weak and strong electric fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about performing perturbation theory for a finite quantum well under an electric field and seeks alternative methods for calculating energy shifts.
  • Another participant references historical treatments of the Quantum-Confined Stark Effect (QCSE) using variational methods, citing specific papers that detail these approaches.
  • A participant mentions having read about variational methods, including one for a triangular potential well, but notes limitations in existing methods for finite wells, particularly regarding strong electric fields.
  • There is a question raised about the accuracy of using an infinite well approximation compared to a finite well in this context.
  • One participant suggests a straightforward approach of calculating the first-order energy shift using the unperturbed wavefunction.
  • A later reply questions which method would be advisable for someone new to the topic, expressing concern that perturbation theory may not adequately address strong fields.

Areas of Agreement / Disagreement

Participants express varying opinions on the suitability of different methods for calculating energy shifts in quantum wells under electric fields. There is no consensus on the best approach, and discussions about the limitations of perturbation theory and variational methods highlight ongoing uncertainty.

Contextual Notes

Participants note that existing variational methods may only apply to weak fields and that calculations for strong fields are complex and not well-documented. There is also uncertainty regarding the accuracy of approximations between infinite and finite wells.

Who May Find This Useful

This discussion may be useful for students and researchers interested in quantum mechanics, particularly those exploring the effects of electric fields on quantum well structures and the associated theoretical methods.

Cerkit
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Hi. Does anyone know how to perform perturbation theory for a finite well under the influence of an electric field?
If not or also what other method is there to calculate the shift in subband energies under the influence of an E field in a quantum well?

Thanks
 
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The very first treatments of the QCSE were performed with variational methods, see for example:

"Band-Edge Electroabsorption in Quantum Well Structures: The Quantum-Confined Stark Effect" by Miller et al. (Phys. Rev. Lett. 53, 2173–2176 (1984)) or the more detailed follow-up paper "Electric field dependence of optical absorption near the band gap of quantum-well structures" also by Miller et al. (Phys. Rev. B 32, 1043–1060 (1985)).

A perturbation approach is given in "A Semi-Empirical Model for Electroabsorption in
GaAsIAlGaAs Multiple Quantum Well Modulator Structures" by Lengyel et al. (IEEE J. Quantum Electron. 26 (1990), p. 296.).
 
Ok. Well as of now I have read through the variational method. I have also found a variational method for a triangle potential well but that is for an infinite well. The only explicit variational method I have found for a finite well is G.Bastard, E.E. Mendez ,Variational calculations on a quantum well in an electric field but the problem with that is that it only gives the calculations for weak fields and says that the expectation values of the hamiltonian for strong fields is not shown because it is too complicated. I am trying to find a fairly simple method which can account for both weak and strong fields. In general I just need an approximation to the perturbation/difference in the energy levels.
 
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Also does anyone have any idea what kind of accuracy can be obtained through using infinite well approximation rather than the finite one?
 
Just do the math, its not that bad. You find the unperturbed wavefunction and calculate first order shift in energy as usual.
 
Which method do you advise me to use as a first timer. Perturbation theory apparently doesn't account for strong fields...?
 

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