An elecetron is placed inside an infite box. Quantum Mechanics

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SUMMARY

An electron placed inside an infinite potential box of width 0.1 nm exhibits quantized energy levels and momentum due to the formation of standing waves, known as harmonics. The fundamental wavelength is critical for calculating the minimum energy and momentum, where the first harmonic corresponds to the ground state of the electron. The relationship L = nλ/2, with n=1 for the fundamental frequency, is essential for deriving these values. This discussion clarifies the concept of standing waves in quantum mechanics and their implications for particle behavior in confined spaces.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with wave-particle duality
  • Knowledge of standing wave formation
  • Basic proficiency in solving quantum equations
NEXT STEPS
  • Research the Schrödinger equation for infinite potential wells
  • Explore the concept of quantum harmonics in more depth
  • Learn about the implications of quantum confinement on electron behavior
  • Study the relationship between wavelength, energy, and momentum in quantum systems
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Students and educators in quantum mechanics, physicists interested in wave-particle duality, and anyone studying the behavior of particles in confined spaces.

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Homework Statement



An e- is placed inside an "infinite box". If the box is .1nm wide, what is the minimum energy and momentum of the e-? Start from the fundamental wavelength and prove the equation you are using to calculate the energy and momentum.

Homework Equations





The Attempt at a Solution



Wait... What's the fundamental wavelength business?
 
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The electron in a box forms standing waves. These standing waves are called harmonics. The first harmonic is called the fundamental frequency and corresponds to the electron's ground state.

I wouldn't call that box "infinite" though.
 
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Ah cool. Then n=1 and

L=nλ/2

I got it from there. Thanks.
 

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