Oscillation frequency of probability density P(x,t)

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SUMMARY

The discussion centers on the oscillation frequency of the probability density P(x,t) for an electron in an infinite 1-D square well of width L. It concludes that for any energy state n, the oscillation frequency is zero due to the nature of stationary states, where the term eiωt vanishes when squared. This indicates that the probability density does not oscillate over time in stationary states.

PREREQUISITES
  • Understanding of quantum mechanics concepts, particularly stationary states.
  • Familiarity with the infinite 1-D square well model.
  • Knowledge of wave functions and their time evolution.
  • Basic grasp of complex numbers and their applications in quantum mechanics.
NEXT STEPS
  • Study the implications of stationary states in quantum mechanics.
  • Explore the mathematical derivation of wave functions in the infinite 1-D square well.
  • Learn about the role of complex exponentials in quantum mechanics.
  • Investigate the concept of probability density and its significance in quantum systems.
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Students and professionals in quantum mechanics, physicists studying wave functions, and anyone interested in the behavior of particles in potential wells.

nhk150709
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If an electron is in an infinite 1-D square well of width L, how do you get oscillation frequency of the probability density for any energy state n?
 
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nhk150709 said:
If an electron is in an infinite 1-D square well of width L, how do you get oscillation frequency of the probability density for any energy state n?

You think about the meaning of the phrase "stationary state" ... :wink:
 
SpectraCat said:
You think about the meaning of the phrase "stationary state" ... :wink:

stationary state... I didn't understand that term till I found e^iwt disappear when it is squared.

so frequency has to be 0.

Thanks ^^
 

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