Normaliztion of the wavefunction mathematics problem

Click For Summary
SUMMARY

The discussion focuses on the normalization of the wavefunction in quantum mechanics, specifically addressing the integral of the exponential function in relation to the wavefunction's amplitude, A. The user questions why the absolute value of A is squared and why it is represented as two times |A|^2 in the normalization process. The confusion arises from the treatment of the exponential function within the integral, particularly regarding the handling of the absolute value in the exponent. This highlights the importance of understanding the mathematical foundations of quantum mechanics.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wavefunctions
  • Familiarity with integrals and their properties in calculus
  • Knowledge of complex numbers and their absolute values
  • Basic grasp of exponential functions and their applications in physics
NEXT STEPS
  • Study the normalization conditions for wavefunctions in quantum mechanics
  • Learn about the properties of integrals involving complex functions
  • Explore the significance of absolute values in quantum mechanics
  • Review the mathematical derivation of the Born rule in quantum mechanics
USEFUL FOR

Students of quantum mechanics, physicists, and anyone interested in the mathematical foundations of wavefunction normalization.

Normalization
Messages
23
Reaction score
0
All the relevant information about the problem is in the attachment.
I just have a problem with the first step, my question it:
How is b true? I would have thought that the second part of the exponential function would be taken outside of the integral as well as A since you're taking the integral with respect to x and why is it TWO TIMES abs(A)^2 and why does the absolute value disappear from the exponent of the integrand?

PS: This is my first time on the forum so I appologize in advance if I haven't been clear enough etc. Also I'm trying to teach myself so I don't have a professor to turn to etc.
 

Attachments

  • Question.JPG
    Question.JPG
    8.1 KB · Views: 381
Physics news on Phys.org
nvm its fine :D
 

Similar threads

Confusion In Writing Identical Particle Wavefunctions
  • · Replies 12 ·
Replies
12
Views
2K
Show that energy E always exists such that junction conditions have a solution
  • · Replies 5 ·
Replies
5
Views
2K
Normalisation of the radial wavefunction in 2s state?
  • · Replies 1 ·
Replies
1
Views
4K
Hydrogen Atom: Wavefunction collapse after measurement of Lz
  • · Replies 20 ·
Replies
20
Views
3K
A strange wave function of the Hydrogen atom
  • · Replies 5 ·
Replies
5
Views
2K
How to find the time-independent (unnormalized) wavefunction
  • · Replies 1 ·
Replies
1
Views
2K
High School A stupidly basic question about expectation value
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Spin and wavefunction of excitons
  • · Replies 2 ·
Replies
2
Views
2K
Time Dependent Wavefunction in Infinite Square Well
  • · Replies 8 ·
Replies
8
Views
5K
Dirac notation - expectation value of kinetic energy
  • · Replies 6 ·
Replies
6
Views
6K