Calculating Energies in Box Potential

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SUMMARY

The discussion focuses on calculating energy levels for two systems within a box potential, specifically for an electron in a box of size a = 10E-10 m and a 1 g metallic sphere in a box of size a = 10 cm. The energy levels are derived using the formula E1 = (h^2) / (8 * m * L^2), where L represents the box size. The quantum effects are significant for the electron due to its small mass and the corresponding energy quantization, while they are negligible for the metallic sphere due to its larger mass and size.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly the box potential model.
  • Familiarity with the Planck constant (h) and its application in energy calculations.
  • Knowledge of mass-energy equivalence and its implications in quantum systems.
  • Basic proficiency in unit conversions between electron volts and joules.
NEXT STEPS
  • Explore the derivation of energy levels in quantum mechanics using the particle in a box model.
  • Investigate the significance of quantum effects in macroscopic versus microscopic systems.
  • Learn about the implications of size and mass on energy quantization in quantum systems.
  • Study the differences between classical and quantum mechanics in terms of particle behavior in potential wells.
USEFUL FOR

Students of quantum mechanics, physicists interested in quantum systems, and educators teaching advanced physics concepts related to energy quantization and box potentials.

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Homework Statement



Consider the box potential
V (x) = 0 0 < x < a
1 elsewhere

a) Estimate the energies of the ground state as well as those of the First and second
excited states for
i) an electron enclosed in a box of size a = 10E-10 m. Express your answer in
electron volts.
ii) a 1 g metallic sphere which is moving in box of size a = 10 cm. Express your
answer in joules.
b) Discuss the importance of quantum effects for both these two systems.

Homework Equations



E1 = ((h)^2 ) / ( 8 * m * L ^2)

En = n^2 * E1

The Attempt at a Solution



The First problem is , I am not sure about L(Length) . Is this equal to the size of the box 'a' in part i and ii.

The Second Problem is how can i define the importantance of quantum effect (b) .. I mean should i have to define with the varying size what change i am observing in Energy Levels .
 
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May be i have to put this one in Advance Physics Sections :-)
 

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