Computing Normalisation Constant A

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Homework Help Overview

The problem involves calculating the normalization constant for a wavefunction defined as Fi = A exp[b*mod(x)], where b is a non-zero positive constant. The normalization condition requires integrating the square of the wavefunction over the entire real line.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to handle the mod(x) term in the wavefunction. Some participants suggest clarifying the meaning of mod(x) as the absolute value of x and recommend splitting the integral into two parts based on the sign of x.

Discussion Status

Participants are actively discussing the interpretation of the mod(x) term and its implications for setting up the integral. Hints have been provided to guide the original poster towards a potential approach, but no consensus or resolution has been reached yet.

Contextual Notes

The discussion includes the need to integrate over the entire real line, which may require careful consideration of the behavior of the wavefunction at negative and positive values of x.

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Homework Statement



Question: Given that Wavefunction Fi = A exp[b*mod(x)], which b is a non zero positive constant. Calculate the normalisation constant.

Homework Equations



1 = Integrating Mod square (Wavefunction) from minus infinity to positive infinity

The Attempt at a Solution



It's the mod(x) there which I don't really know how to deal with it. Could anyone please help me out? Many Thanks!
 
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By mod(x) do you mean the absolute value of x- |x|?

If so

HINT: Remember that |x|=-x if x<0 and |x|= x if x>0.

Use this fact and split the integral into the sum of two integrals, one from [itex]-\infty[/itex] to 0 and the other from 0 to [itex]\infty[/itex].
 
G01 said:
By mod(x) do you mean the absolute value of x- |x|?

If so

HINT: Remember that |x|=-x if x<0 and |x|= x if x>0.

Use this fact and split the integral into the sum of two integrals, one from [itex]-\infty[/itex] to 0 and the other from 0 to [itex]\infty[/itex].


Thanks a lot, I think I've got it now!

Cheers!
 
No problem! :smile:
 

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