Ground and Excited States in a Potential Well (QM)

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SUMMARY

The discussion focuses on the ground and excited states of a quantum particle in an infinite potential well, specifically addressing the behavior of wave functions at different energy levels. The ground state wave function is described as resembling a Gaussian distribution, while excited states manifest as sine waves with varying frequencies. Participants debate the relationship between amplitude and frequency in relation to energy levels, particularly at the potential jump located at 2a. The significance of the energy level being zero is also questioned, emphasizing the constraints of quantum mechanics regarding energy states.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wave functions
  • Familiarity with the concept of potential wells in quantum systems
  • Knowledge of sine wave properties and their relationship to energy levels
  • Basic grasp of Gaussian distributions and their applications in quantum states
NEXT STEPS
  • Study the mathematical formulation of wave functions in infinite potential wells
  • Explore the concept of energy quantization in quantum mechanics
  • Learn about the significance of potential energy jumps in quantum systems
  • Investigate the implications of boundary conditions on wave functions
USEFUL FOR

Students and professionals in physics, particularly those specializing in quantum mechanics, as well as educators seeking to clarify concepts related to wave functions and potential wells.

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Here's the problem:

http://www.phys.washington.edu/users/karch/324/2007/hw3.pdf

Just the first one.

Okay, so my understanding is that the first state of Psi (ground state) is just an arc, like a Gaussian distribution, starting from 0 at E0 and finishing at 5a also at the level of E0.

The next ones are just sine waves at higher frequencies.

So would I just draw a high frequency sine wave of amplitude E0 until I get to the "jump" at 2a, and then just decrease the the amplitude that that point, but keep the frequency the same?

Or since the frequency corresponds to energy, and I don't have as much of a jump from E0 to the bottom of the well, I should keep the amplitude constant the whole time, but decrease the frequency once I get to the "jump" at 2a?

The book only mentions an infinite square well and doesn't really go into it.
 
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Sorry, but I still haven't figured this one out.

Is the energy level 0 meaningless here, since a particle can't get below the ground state (E0) in energy?

So it would be a high-frequency sine wave with the amplitude being from E to E0? I still don't see the significance of the potential jump in the middle.
 

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