Analytical solution for bound state energies of infinite well

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SUMMARY

The discussion focuses on finding bound state energies for an infinite potential well by solving the equation E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2. The goal is to identify intersection points between the right-hand side (RHS) and left-hand side (LHS) curves, which correspond to the energy levels (n). Participants suggest using tools like MATLAB or Mathematica for this analytical solution, emphasizing the need for clarity in defining the potential involved.

PREREQUISITES
  • Understanding of quantum mechanics concepts, specifically bound states and potential wells.
  • Familiarity with mathematical functions such as tangent and square root.
  • Proficiency in using MATLAB or Mathematica for numerical analysis.
  • Knowledge of the constants involved, including Planck's constant (hbar) and mass (m).
NEXT STEPS
  • Learn how to implement numerical solutions in MATLAB for solving transcendental equations.
  • Explore Mathematica's capabilities for plotting functions and finding intersections.
  • Study the mathematical derivation of energy levels in quantum mechanics for infinite potential wells.
  • Investigate the differences between finite and infinite potential wells in quantum mechanics.
USEFUL FOR

Students and researchers in quantum mechanics, physicists working on potential wells, and anyone interested in computational methods for solving quantum energy problems.

Bob007
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Hi there
I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as:
E^1/2 tan(2ma^2E/4hbar)^1/2 = (V0-E)^1/2
If solved properly, it should give one curve (RHS), crossed by several LHS curves. Intersection points are the answers I am looking for. Each intersection corresponds to one n. I am wondering if it can be done by Matlab or Mathematica? Sorry if it is too basic :)
Thanks
 
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Bob007 said:
assuming infinite potential
That doesn't specify what the potential is! Assuming infinite potential where?

Also you can't solve RHS and LHS of an equation, you solve the equation itself!

Your explanations are inadequate and unclear!
 
Bob007 said:
I am trying to find bound state energies assuming infinite potential.

Do you mean the finite or the infinite potential well?
 

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