Go to the U of M home page
School of Physics & Astronomy
School of Physics and Astronomy Wiki

User Tools

Trace: • q_a_1012 • lec_notes_1012
classes:2009:fall:phys4101.001:q_a_0918

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revisionPrevious revision
Next revision		Previous revision
classes:2009:fall:phys4101.001:q_a_0918 [2009/09/18 09:28] – x500_maxwe120classes:2009:fall:phys4101.001:q_a_0918 [2009/09/26 23:43] (current) – yk
Line 57: Line 57:
 === Zeno 9:10 9/18 === === Zeno 9:10 9/18 ===
 This is a very interesting concept. I also don't understand it entirely either. In reference to the The Schrodinger Equation for the Harmonic Oscillator [2.70], I understand that the equation is "unstable" for many solutions. The general power series solution developed is essentially a sum of weighted decaying exponentials, and a finite series is needed to integrate a finite probability density (which is later normalized); and I see proof in figure [2.6] that eqn [2.83] must hold for all normalizable (physically real) solutions, so my corollary question is: do non-normalizable solutions (those that blow up to +/- <math>\infty</math>) to the Schrodinger Equation have any physical significance? Or are they born out of the thoroughness of mathematics and completely thrown away? This is a very interesting concept. I also don't understand it entirely either. In reference to the The Schrodinger Equation for the Harmonic Oscillator [2.70], I understand that the equation is "unstable" for many solutions. The general power series solution developed is essentially a sum of weighted decaying exponentials, and a finite series is needed to integrate a finite probability density (which is later normalized); and I see proof in figure [2.6] that eqn [2.83] must hold for all normalizable (physically real) solutions, so my corollary question is: do non-normalizable solutions (those that blow up to +/- <math>\infty</math>) to the Schrodinger Equation have any physical significance? Or are they born out of the thoroughness of mathematics and completely thrown away?
 +===spillane 9-18====
 +Correct me if im wrong but, isnt a fundemental constraint on Hookes law: that the pertubations of x most relatively small. That being said how is it in the analytical method  between 2.73 and 2.74 we now change this condition by allowing x to be very large in order to simplify the expression. Isnt this a contradiction? How is this valid?
 +Is it related to the graph 2.6 and the fact that eq. 2.70 has linearly independent solutions for any value of E but,  almost all of this solutions blow up exponentially at large x?
 +WHATS GOING ON?
 +===John Galt 10:27 9/18===
 +I am also not completely positive, but isn't the reason you need to have a E=.5h(bar)w value due to the fact that the power series in EQ. 2.79 blows up at other values? If so, it is just how the math works. I am not sure how to describe it in a qualitative or visual sense, I guess. I'm guessing that the math tools were chosen to follow the experimentally observed events, so a proper function had to be determined which would only allow probability functions to exist in places where the particle could actually be, so 2.6 is probably just showing that, yes, as a visual confirmation, En = (n+1/2)h(bar)w.
 +
 +==== time to move on ====
 +
 +It's time to move on to the next Q_A: [[Q_A_0921]]
classes/2009/fall/phys4101.001/q_a_0918.1253284136.txt.gz · Last modified: 2009/09/18 09:28 by x500_maxwe120

Page Tools