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--- classes:2009:fall:phys4101.001:q_a_0918 [2009/09/18 07:44] – x500_spil0049
+++ classes:2009:fall:phys4101.001:q_a_0918 [2009/09/26 23:43] (current) – yk
@@ Line 47: / Line 47: @@
 The time independent schr. eq. is a linear eq but,in contrast to the schr eq., it contains explicitly the total energy E. Therefore, an arbitrary linear combination of diff. solutions will satisfy the equation only if they all correspond to the same value of E. Definite total energy follows from the fact that separation of variables is the tool used to get schr. eq.
 It is one of the answers to "Whats so great about separable solutions"pg 26 Griffiths.
 ====Pluto 4ever 10:11pm 9/17/09====
 On pg. 54 it talks about how the Schrodinger equation for the harmonic oscillator can give solutions for any value of //E// but only the values for //E// defined by <math>E_n=(n+1/2)\hbar\omega</math> can produce normalizable solutions. Meaning any value in between them will blow up. Maybe I'm reading this wrong but I just want to know how that works.
+====spillane 8ish 9/18====
+Im also fuzzy on this.  fig. 2.6????
+=== Mercury 8:11 09/18/2009 ===
+I'm also having problems understanding this concept and the plots in fig. 2.6.
+=== 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?
+===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]]

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