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March 28, 2026The Chemical Educator

Particle a in One-Dimensional Finite and Semi-Infinite Well Revisited

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Authors

EPEnrique Peacock-López

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Overview

This research revisits quantum energy levels in finite and semi-infinite wells, suggesting new ways to calculate outcomes.

Key Points

  • The study aims to explore the energy levels of a quantum particle in both finite and semi-infinite wells using a new approach.
  • Scaled space and energy to derive a dimensionless Schrodinger equation
  • Solved for the square root of dimensionless energies
  • Defined classes of wells based on well depth
  • Derived transcendental equations for energy levels
  • Obtained expressions for wave functions
  • Identified the maximum number of energy levels easily
  • Derived a simple expression for wave functions
  • Showed that dimensionless energies correspond to solutions of transcendental equations

Cite This Study

Enrique Peacock-López (2011) studied this question.

synapsesocial.com/papers/69c771688bbfbc51511e15e6https://doi.org/10.1333/s00897112370a
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Also Consider

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  4. 4Matrix Mechanics of a Particle in a One-Dimensional Infinite Square Well2024
  5. 5Matrix Mechanics of a Particle in a One-Dimensional Infinite Square Well2024 · 1 citations