Normalise Wave Packet psi(x) to Unity

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SUMMARY

The wave packet psi(x, t=0) is defined as C*exp(i*p0*x/hbar)*exp(-[x]/(2*deltax)). To normalize psi(x) to unity, one must compute the integral of |psi|^2 over the entire space, which involves evaluating the integrals from negative to positive infinity. The initial calculation incorrectly resulted in zero, indicating a misunderstanding of the integral's evaluation. The correct approach reveals that C is not a complex number but rather a real constant that can be determined through proper integration techniques.

PREREQUISITES
  • Understanding of quantum mechanics concepts, specifically wave packets.
  • Familiarity with normalization in quantum mechanics.
  • Knowledge of complex exponentials and their properties.
  • Ability to perform definite integrals, particularly involving exponential functions.
NEXT STEPS
  • Review the process of normalizing wave functions in quantum mechanics.
  • Learn about the properties of complex numbers in quantum mechanics.
  • Study integration techniques for exponential functions, especially in the context of quantum mechanics.
  • Explore the implications of normalization on physical interpretations of wave packets.
USEFUL FOR

This discussion is beneficial for students in introductory quantum mechanics courses, particularly those studying wave packets and normalization techniques. It is also useful for educators and anyone seeking to clarify the mathematical foundations of quantum wave functions.

ak416
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consider the wave packet psi(x, t=0) = C*exp(i*p0*x/hbar)*exp(-[x]/(2*deltax))
where C is the normalisation constant
part a) normalise psi(x) to unity
I took Integral from negative infinity to positive infinity of ([psi]^2)dx and got [C]^2 * ( Integral from negative infinity to 0 of exp(x/deltax)dx + Integral from 0 to positive infinity of exp(-x/deltax)dx )
However this gives me [C]^2 * 0 and there is no number for C that i can think of that can make it equal to 1. I am thinking C must be some complex number, but i don't know where to go from here...
Note: this is for a introductory QM class
 
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You did the integrals wrong. The result is not 0.
 

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