Complexity of Solving Multi-Potential Schrodinger Equation?

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SUMMARY

The discussion focuses on solving the Schrödinger equation for a piecewise potential defined by three regions: V1 for 0 PREREQUISITES

  • Understanding of quantum mechanics principles, specifically the Schrödinger equation.
  • Familiarity with piecewise potential functions and their implications in quantum systems.
  • Knowledge of boundary conditions and their role in determining wavefunction continuity.
  • Experience with solving differential equations relevant to quantum mechanics.
NEXT STEPS
  • Study the method of matching boundary conditions in quantum mechanics.
  • Learn about energy eigenvalues in piecewise potential problems.
  • Explore the implications of constant potential regions on wavefunction behavior.
  • Review examples of solving the Schrödinger equation for multi-region potentials.
USEFUL FOR

Students and researchers in quantum mechanics, particularly those tackling problems involving piecewise potentials and energy eigenvalue calculations.

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Homework Statement


Does anyone now how to solve the Schrödinger equation for a potenital such that: V1(0<x<a), v2(a<x<b), v3(b<x<c). Also i need to write down the condition which gives the possible energy eigenvalues of a particle in the potential. ITs easily to solve the first potential well but when it starts to introducing the two others I feel like I am messing up. Any help would be nice?


Homework Equations





The Attempt at a Solution


 
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You basically do what you would do in a square well, except that you match the wavefunctions at the boundaries. (I'm assuming that v1, v2 and v3 are constants.)
 

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