"Quantum scattering"의 두 판 사이의 차이
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<h5>introduction</h5> | <h5>introduction</h5> | ||
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+ | * <math>\varphi_{xx}+(\lambda-u)\varphi=0</math> | ||
+ | * looking for bounded functions on the whole line<br> | ||
+ | ** If the interval is unbounded, or if the coefficients have singularities at the boundary points, one calls L singular. In this case the spectrum does no longer consist of eigenvalues alone and can contain a continuous component. There is still an associated eigenfunction expansion (similar to Fourier series versus Fourier transform). This is important in quantum mechanics, since the one-dimensional Schrödinger equation is a special case of a S–L equation | ||
+ | * discrete spectrum <math>\lambda<0</math> | ||
+ | * continuous spectrum <math>\lambda>0</math> | ||
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2011년 2월 7일 (월) 09:56 판
introduction
- \(\varphi_{xx}+(\lambda-u)\varphi=0\)
- looking for bounded functions on the whole line
- If the interval is unbounded, or if the coefficients have singularities at the boundary points, one calls L singular. In this case the spectrum does no longer consist of eigenvalues alone and can contain a continuous component. There is still an associated eigenfunction expansion (similar to Fourier series versus Fourier transform). This is important in quantum mechanics, since the one-dimensional Schrödinger equation is a special case of a S–L equation
- discrete spectrum \(\lambda<0\)
- continuous spectrum \(\lambda>0\)
history
encyclopedia
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- http://www.scholarpedia.org/
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- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
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