Calculate 1st 3 Energy Levels for Electron in Quantum Well

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SUMMARY

The discussion focuses on calculating the first three energy levels for an electron in a quantum well with a width of 10 Angstroms and infinite walls. The energy levels are derived using the formula En = (n²π²ħ²)/(2mL²), where m is the electron mass (9.109E-31 kg), L is the well width (10E-10 m), and ħ is the reduced Planck's constant (1.055E-34 J·s). The calculated energy levels yield En = n² * 6.032E-20 J for n = 1, 2, and 3. The discussion also addresses unit conversion, clarifying that kg·m²/s² equates to Joules.

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  • Understanding of quantum mechanics principles
  • Familiarity with the concept of quantum wells
  • Knowledge of the reduced Planck's constant (ħ)
  • Basic proficiency in unit conversion and dimensional analysis
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  • Learn about the implications of infinite potential barriers in quantum mechanics
  • Explore the concept of wave functions in quantum mechanics
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Students and professionals in physics, particularly those studying quantum mechanics, as well as engineers working with semiconductor technologies and quantum well applications.

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Homework Statement


Calculate the first three energy leveles for an electron in a quantum well of width 10Angstrom
and infinite walls.


Homework Equations



[tex]E<sub>n</sub>=\frac{n<sup>2</sup>pi<sup>2</sup>(hbar)<sup>2</sup>}{2mL<sup>2</sup>}[/tex]

The Attempt at a Solution


m=9.109E-31Kg
L=10E-10m
hbar=1.055E-34
En=n2*6.032E-20

My problem is really with the unit though.

here is what I have

[tex]\frac{Kgm<sup>2</sup>}{s}*\frac{Kgm<sup>2</sup>}{s}*\frac{1}{Kg}*\frac{1}{m<sup>2</sup>}=[/tex][tex]\frac{Kgm<sup>2</sup>}{s<sup>2</sup>}[/tex]
 
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In TeX, you don't use the sup tags. To get a superscript, use ^, e.g. n^2 for n2.

What's the specific problem you have with the units? A kg m2/s2 is a Joule.
 

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