Electron in infinite well equation

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SUMMARY

The energy of the ground state for an electron confined in an infinitely deep well of width 0.1 nm can be calculated using the formula E=(n^2 hbar^2 ∏^2)/(2m L^2). In this context, n represents the quantum number, hbar is the reduced Planck's constant, m is the mass of the electron, and L is the width of the well. For the ground state, n equals 1, making this equation essential for determining the energy in electron volts (eV).

PREREQUISITES
  • Understanding of one-dimensional quantum mechanics
  • Familiarity with the reduced Planck's constant (hbar)
  • Knowledge of the mass of an electron
  • Basic grasp of quantum numbers
NEXT STEPS
  • Calculate the ground state energy using the formula E=(n^2 hbar^2 ∏^2)/(2m L^2)
  • Explore the implications of quantum confinement on electron behavior
  • Study the differences between one-dimensional and three-dimensional quantum wells
  • Investigate the applications of quantum wells in modern technology
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics and semiconductor physics, will benefit from this discussion.

ZedCar
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Homework Statement



An electron is confined in an infinitely deep well of width 0.1nm, about the size of an atom. Estimate the energy of the ground state in eV.

Homework Equations



Is this the equation I should be using?

E=(n^2 hbar^2 ∏^2)/(2m L^2)



The Attempt at a Solution

 
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ZedCar said:
Is this the equation I should be using?
Yes, assuming you're using 1-dimension. (The way the problem statement was worded, it sounds to me like 1-dimensional quantum mechanics is a reasonable assumption.)
 

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