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| classes:2009:fall:phys4101.001:q_a_0923 [2009/09/23 18:48] – yk | classes:2009:fall:phys4101.001:q_a_0923 [2009/09/26 23:37] (current) – yk |
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| <math>G(x_0)>0</math>, or else <math>G(x)\equiv0</math>, can't be normalized. Then <math>G(x_1)+G(x_2)\ge2G(x_0)>0</math>. | <math>G(x_0)>0</math>, or else <math>G(x)\equiv0</math>, can't be normalized. Then <math>G(x_1)+G(x_2)\ge2G(x_0)>0</math>. |
| Now let <math>x_1\rightarrow-\infty</math>, <math>x_2\rightarrow+\infty</math>, in order to satisfy the above eqation <math>G(x_1\rightarrow-\infty)</math>,<math>G(x_2\rightarrow+\infty)</math> cannot be 0 at the same time, so the integral <math>\int |\psi(x)|^2\,dx=\int G(x)\,dx</math> will go to infinity, cannot be normalized. | Now let <math>x_1\rightarrow-\infty</math>, <math>x_2\rightarrow+\infty</math>, in order to satisfy the above eqation <math>G(x_1\rightarrow-\infty)</math>,<math>G(x_2\rightarrow+\infty)</math> cannot be 0 at the same time, so the integral <math>\int |\psi(x)|^2\,dx=\int G(x)\,dx</math> will go to infinity, cannot be normalized. |
| ====Andromeda==== | ====Andromeda 16:50 9/22==== |
| is there any relation between Hermite polynomial and Legendre polynomial??? | is there any relation between Hermite polynomial and Legendre polynomial??? |
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| ==Schrodinger's Dog== | ===Schrodinger's Dog 21:11 9/22=== |
| No, although they both are recursive relations of sorts, they aren't related in any way. But, Hermite Polynomials are special cases of Laguerre polynomials, if your interested in looking into that. | No, although they both are recursive relations of sorts, they aren't related in any way. But, Hermite Polynomials are special cases of Laguerre polynomials, if your interested in looking into that. |
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| ====Hardy 9/22 19:02==== | ====Hardy 9/22 19:02==== |
| I do not quite understand why the <math>a_-\psi_0(x)</math> should be zero. Can it be some value between zero and <math>\frac{1}{2}\hbar\omega</math>? | I do not quite understand why the <math>a_-\psi_0(x)</math> should be zero. Can it be some value between zero and <math>\frac{1}{2}\hbar\omega</math>? |