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--- classes:2009:fall:phys4101.001:lec_notes_1026 [2009/10/27 23:52] – x500_choxx169
+++ classes:2009:fall:phys4101.001:lec_notes_1026 [2009/10/28 10:21] (current) – x500_stans028
@@ Line 27: / Line 27: @@
-(B) Always transmission/reflection
+(B) Always transmission/reflection (In 2D/3D => scattering)
- In 2D/3D ==> scattering
 (C) Depends on
@@ Line 74: / Line 72: @@
 <math>\ f_p(x) = 1/sqrt(2*pi*hbar)*exp(i*E/hbar*x) </math>
--> normalization => <math>\int f_p^* (x)*f_p(x) dx</math> = A *  <math>\delta</math> )p-p'
+-> normalization => <math>\int f_p^* (x)*f_p(x) dx</math> = A *  <math>\delta</math> (p-p')
 -> <math>\1/sqrt(2*pi*hbar)</math> is corresponded to the value A
-Finally, a question was raised concerning notation used in section 3.4 of Griffiths.  The question related to equation 3.43 on page 106.  What is the difference between f<sub>n</sub> and Ψ?  It should be noted that equation 3.43 is Fourier's trick in bracket notation.  f<sub>n</sub> is any function that is any stationary state wave function.  You could also think of f<sub>n</sub> as the initial state of a wave function.  Ψ is the time-dependent wave function of the system.
+Finally, a question was raised concerning notation used in section 3.4 of Griffiths.  The question related to equation 3.43 on page 106.
+<math> c_n = <f_n|\Psi> </math>.
+What is the difference between f<sub>n</sub> and Ψ?  It should be noted that equation 3.43 is Fourier's trick in bracket notation.
+f<sub>n</sub> is any function that is any stationary state wave function.  You could also think of f<sub>n</sub> as the initial state of a wave function.
+Ψ is the time-dependent wave function of the system.
+<math> \Psi(x,t) = \sum c_n * f_n(x) </math>

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