QM beginner's question about deltafunction potential problem

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SUMMARY

The discussion focuses on determining the number of bound states for a particle under a delta function potential. The process involves writing Schrödinger's equation and solving it with specific boundary conditions: the wavefunction must be continuous at x=0, while its derivative experiences a discontinuity. The conclusion is that there is only one bound state for a particle in this potential when the energy is less than zero (E<0).

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically bound states.
  • Familiarity with Schrödinger's equation and its applications.
  • Knowledge of delta function potentials and their implications in quantum systems.
  • Ability to analyze wavefunctions and boundary conditions in quantum mechanics.
NEXT STEPS
  • Study the derivation of bound states in quantum mechanics using delta function potentials.
  • Learn about the implications of boundary conditions on wavefunctions in quantum systems.
  • Explore the mathematical techniques for solving Schrödinger's equation in one-dimensional potentials.
  • Investigate other types of potentials and their bound state solutions for comparative analysis.
USEFUL FOR

Students of quantum mechanics, physicists interested in potential theory, and anyone studying bound states in quantum systems will benefit from this discussion.

runninglow
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how can i know the number of boundstate of a particle acting under a deltafunction potential?
 
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Draw the wavefunction. How many ways are there to do this?
 
Or if you want to go the whole nine

1) Write Schrödinger's equation
2) Solve Schrödinger's equation with the appropriate boundary conditions (Psi continuous at x=0, dPsi/dx discontinuous by a certain amount), and the condition that E<0
3) Show that there is in fact only one such state
 

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