Understanding Normalization Factors in Scientific Research

  • Context: Graduate 
  • Thread starter Thread starter M. next
  • Start date Start date
  • Tags Tags
    Normalization
Click For Summary

Discussion Overview

The discussion revolves around the mathematical simplifications and normalization factors in scientific research, specifically focusing on the expression involving the exponential function and its implications in integrals. Participants express confusion regarding the mathematics involved and seek clarification on specific steps.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the mathematical simplifications related to a figure and asks for clarification.
  • Another participant questions the equivalence of the expression [exp(-x^2)]^2 and seeks to establish its value.
  • Some participants propose that [exp(-x^2)]^2 equals exp(-x^4), while others challenge this assertion.
  • There is a discussion about the properties of the exponential function, with one participant stating that exp(a) = e^a and exploring the implications of multiplying two exponential terms.
  • One participant asserts that the correct simplification leads to e^2a, while another participant questions this claim.
  • A later reply emphasizes that the integral of exp[-x^2] is defined only from -infinity to infinity, suggesting a limitation in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the mathematical simplifications, with multiple competing views presented regarding the equivalence of the expressions and the properties of the exponential function.

Contextual Notes

There are unresolved mathematical steps and assumptions regarding the definitions of the exponential function and its properties, which contribute to the confusion in the discussion.

M. next
Messages
380
Reaction score
0
How is it that:

See figure:

Given: See figure too

In details, I don't get the maths and simplification that took place!
Thanks!
 

Attachments

  • Nor.PNG
    Nor.PNG
    3.4 KB · Views: 565
  • Eqqqq.PNG
    Eqqqq.PNG
    2.1 KB · Views: 524
Physics news on Phys.org
Well, what is [exp(-x^2)]^2 equal to ?
 
exp(-x^4)
 
Remember, exp(a) = e^a. So exp(a)exp(a) = (e^a)(e^a) = ... ?
 
it is supposed to be e^2a.
Correct me if am wrong.
 
Right. So that should tell you what [e^(-x^2)][e^(-x^2)] is.
 
woah get your math straight.
that's not true: exp(a^2) =(e^a)(e^a)
the integral of exp[-x^2] is defined only from -infinity to infinity.
 

Similar threads

Undergrad Derivation of normal Zeeman-Effect
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Qubits state calculation
  • · Replies 6 ·
Replies
6
Views
2K
Graduate How to derive the quantum detailed balance condition?
  • · Replies 0 ·
Replies
0
Views
1K
Graduate Normalization of Morse potential wavefunctions
  • · Replies 5 ·
Replies
5
Views
2K
Final project ideas using Noether's theorem in simulation class
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Prof Mike Wiest's proposed link between quantum and consciousness
  • · Replies 19 ·
Replies
19
Views
3K
Undergrad (Baby QM) Analytic Solution to the Infinite Square Well Problem
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Relationship between Wilson's RG and the Callan-Symanzik Equation
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Comparing Information Loss: Time Dilation vs. Decoherence
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Is Normalizing a 4x4 Matrix Possible Using Multiple Methods?
  • · Replies 2 ·
Replies
2
Views
3K