How Does Resizing an Infinite Square Well Affect Ground State Probability?

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SUMMARY

The discussion focuses on the quantum mechanics problem of a particle in an infinite square well, initially confined between x=0 and x=L/2, and subsequently expanded to x=L. The key task is to determine the probability of the particle being in the ground state of the expanded well after the walls are moved. Participants emphasize the necessity of first calculating the wavefunction for the narrower well, normalizing it, and then determining the overlap with the ground state wavefunction of the wider well, which is essential for finding the probability.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically infinite square wells.
  • Familiarity with wavefunctions and their normalization.
  • Knowledge of ground state properties in quantum systems.
  • Ability to compute probability amplitudes and overlaps between states.
NEXT STEPS
  • Study the normalization process of wavefunctions in quantum mechanics.
  • Learn about the mathematical formulation of infinite square wells in quantum mechanics.
  • Explore the concept of probability amplitudes and their significance in quantum state transitions.
  • Investigate the implications of sudden changes in potential wells on quantum states.
USEFUL FOR

Students and educators in quantum mechanics, physicists working with quantum systems, and anyone interested in the mathematical aspects of wavefunctions and state probabilities in quantum mechanics.

cragar
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Homework Statement


we have a particle in an infinite square well from x=0 to x=L/2
Then it says that we suddenly move the right hand side of the wall to x=L
and then it asks to find the probability that the particle is in the ground state of the widened well.

The Attempt at a Solution


Would I first find the wavefunction for the narrow well and then normalize it, and then normalize this again for the wider well.
 
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Are you sure they didn't specify the state of the particle in smaller square well? Did they say it's in the ground state of the smaller well? You certainly need to know that before you can compute the overlap with the ground state in the larger square well.
 
ya sorry they said it was in the ground state of the smaller well and they gave me the wave function for it.
 

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