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p. 12 Introduction to Quantum Mechanics by Griffiths

Equation 1.25: the differential operatot was factored. This to me seems like a mathematical trick or due to amazing foresight, but is there any underlying/guiding theory for this factorisation?

Equation 1.27: the wavefunction was assumed to be zero at infinity which to me seems a bit weird, since by this assumption we enforced normalizability and got the answer we fabricated, so is my criticism valid? Is there a more rigorous proof?

The image of the book is enclosed below.

Thanks :)

<a href='http://i.imgur.com/WSUwLhM' title=''><img src='http://i.imgur.com/WSUwLhM.jpg' alt='' title='Hosted by imgur.com' /></a>

(I don't know why the image thumbnail isn't working)

[PLAIN]http://<a [Broken][/PLAIN] [Broken] href='http://i.imgur.com/WSUwLhM' [Broken][/PLAIN] [Broken] title=''><img src='http://i.imgur.com/WSUwLhM.jpg' alt='' title='Hosted by imgur.com' /></a>[/PLAIN] [Broken]

[PLAIN]http://<a [Broken][/PLAIN] [Broken] href='http://i.imgur.com/WSUwLhM' [Broken][/PLAIN] [Broken] title=''><img src='http://i.imgur.com/WSUwLhM.jpg' alt='' title='Hosted by imgur.com' /></a>[/PLAIN] [Broken]

Equation 1.25: the differential operatot was factored. This to me seems like a mathematical trick or due to amazing foresight, but is there any underlying/guiding theory for this factorisation?

Equation 1.27: the wavefunction was assumed to be zero at infinity which to me seems a bit weird, since by this assumption we enforced normalizability and got the answer we fabricated, so is my criticism valid? Is there a more rigorous proof?

The image of the book is enclosed below.

Thanks :)

<a href='http://i.imgur.com/WSUwLhM' title=''><img src='http://i.imgur.com/WSUwLhM.jpg' alt='' title='Hosted by imgur.com' /></a>

(I don't know why the image thumbnail isn't working)

[PLAIN]http://<a [Broken][/PLAIN] [Broken] href='http://i.imgur.com/WSUwLhM' [Broken][/PLAIN] [Broken] title=''><img src='http://i.imgur.com/WSUwLhM.jpg' alt='' title='Hosted by imgur.com' /></a>[/PLAIN] [Broken]

[PLAIN]http://<a [Broken][/PLAIN] [Broken] href='http://i.imgur.com/WSUwLhM' [Broken][/PLAIN] [Broken] title=''><img src='http://i.imgur.com/WSUwLhM.jpg' alt='' title='Hosted by imgur.com' /></a>[/PLAIN] [Broken]

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