Normalize Quantum Mechanical Wavefunction

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SUMMARY

The discussion focuses on normalizing a quantum mechanical wavefunction defined as \(\Psi(x) = Ae^{ax}\) for \(x < 0\) and \(\Psi(x) = Ae^{-2ax}\) for \(x > 0\). The normalization process requires integrating the wavefunction piecewise from \(-\infty\) to \(0\) and from \(0\) to \(\infty\), ensuring the total probability equals 1. The constant \(A\) can be determined through these integrals, confirming that piecewise integration is essential for this function.

PREREQUISITES
  • Understanding of quantum mechanics wavefunctions
  • Knowledge of integration techniques in calculus
  • Familiarity with the concept of normalization in probability theory
  • Basic grasp of piecewise functions
NEXT STEPS
  • Learn about the normalization of wavefunctions in quantum mechanics
  • Study integration techniques for piecewise functions
  • Explore the implications of wavefunction normalization on quantum states
  • Investigate the role of constants in quantum mechanical equations
USEFUL FOR

Students of quantum mechanics, physicists working with wavefunctions, and anyone interested in the mathematical foundations of quantum theory will benefit from this discussion.

mju4t
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Homework Statement


A Quantum mechanical particle is defined by the following wave functions:
\Psi(x) = Aeax for x<0
\Psi(x) = Ae-2ax for X>0

where A and a are both real, positive constants.

Normalize the wavefunction, i.e. determine an expression for A in terms of a.


Homework Equations





The Attempt at a Solution



I think to normalize it you have to integrate from the limits and set it equal to 1. However, I'm not sure if you have to do it piecewise, like from -inf to 0 and then again from 0 to inf...

 
Physics news on Phys.org
Hello mju4t
You've got it right, you have to integrate it piecewise. That's how the function is defined.
Good luck.
 

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