"Quantum scattering"의 두 판 사이의 차이

2011년 2월 7일 (월) 09:56 판

\(\varphi_{xx}+(\lambda-u)\varphi=0\)
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 \(\lambda>0\)

@@ 1번째 줄: / 1번째 줄: @@
 <h5>introduction</h5>
+* <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>