Wave in particle in 1 box with infinite potential energy

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SUMMARY

The discussion focuses on the relationship between a particle's kinetic energy and its wave properties in a one-dimensional infinite potential well. When the kinetic energy decreases, the wave's wavelength increases due to the inverse relationship defined by the wavenumber equation \( k = \frac{\sqrt{2m(U-E)}}{\hbar} \). The amplitude is determined by normalization, specifically \( A = (2/L)^{1/2} \), which remains constant regardless of kinetic energy changes. Additionally, the concept of the box "contracting" in the ground state is explored, highlighting the influence of energy levels on wave behavior.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of wave-particle duality
  • Familiarity with the Schrödinger equation
  • Knowledge of normalization techniques in wave functions
NEXT STEPS
  • Study the implications of the Schrödinger equation in infinite potential wells
  • Explore the concept of wavefunction normalization in quantum mechanics
  • Investigate the relationship between kinetic energy and potential energy in quantum systems
  • Learn about the implications of energy quantization in bound states
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Students of quantum mechanics, physicists studying wave-particle interactions, and educators seeking to clarify concepts related to infinite potential wells.

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Homework Statement


Q.1Why when the particle's kinetic energy is smaller, the wave has longer wavelength and higher amplitude?
Q.2 Why the length of box decrease in ground state?

<All in attachment>

Homework Equations





The Attempt at a Solution


Q.1 wavenumber k= \frac{\sqrt{2m(U-E)}}{\hbar}, isn't it?
so KE decreases, wavenumber decreases, wavelength increases?
But isn't the amplitude just (2/L)^(1/2), from the normalization techinque?

Q.2 I really do not know why the box suddenly "contract" in the ground state.
 

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can someone tell me why the amplitude of wave is affected by kinetic energy(E-U)?
 

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