How to find the time-independent (unnormalized) wavefunction

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SUMMARY

The discussion focuses on finding the time-independent (unnormalized) wavefunction, \(\psi_{a}(x)\), for a particle with a known momentum \(p_{x}=\hbar k_{0}\). The problem is derived from Liboff's "Introductory Quantum Mechanics" (4th edition). Participants express difficulty in generalizing the solution without specific momentum values and seek guidance on the relationship between position-space states and momentum states.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically wavefunctions.
  • Familiarity with the concept of momentum in quantum mechanics.
  • Knowledge of the relationship between position-space and momentum-space states.
  • Basic proficiency in using the Fourier transform in quantum mechanics.
NEXT STEPS
  • Study the derivation of wavefunctions from momentum using Fourier transforms.
  • Learn about the implications of the uncertainty principle on wavefunctions.
  • Explore examples of time-independent wavefunctions in one-dimensional quantum systems.
  • Investigate the normalization of wavefunctions and its significance in quantum mechanics.
USEFUL FOR

Students of quantum mechanics, particularly those tackling problems involving wavefunctions and momentum, as well as educators seeking to clarify these concepts in a teaching context.

Mary
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Homework Statement



How would I find the time-independent (unnormalized) wavefunction given the momentum? I don't know if this can be generalized without giving the momentum in the problem. I want to do this problem myself but I'm stuck.

The problem states:

A particle of mass m moves in one dimension (x). It is known that the momentum of the particle is p_{x}=\hbark_{0}, where k_{0} is a known constant. What is the time-independent (unnormalized) wavefunction of this particle, \psi_{a}(x)?

this is only the first part of the problem. If I get past this I believe I can finish the rest.

TextBook Used

Liboff's Introductory Quantum Mechanics 4th edition ...hasn't been that helpful
 
Physics news on Phys.org
If you have a particle prepared in a position-space state ##\psi(x)##, how would you normally go about finding the momentum of the state?
 

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