Unformatted text preview: ). Plot the probability distribution (eigenfunction squared) for the eigenvalues α = 1 and α = 50 (cf. Fig.2.3.2b ). (b) Find the eigenvalues using periodic boundary conditions and compare with Fig.2.3.5 . Problem 3: Use a discrete lattice with 100 points spaced by ‘a’ to solve the radial Schrodinger equation E f(r) = − 2 2m d 2 dr 2 − q 2 4 πε r + ( + 1) 2 2mr 2 ⎛ ⎝ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ f(r) for the 1s and 2s energy levels of a hydrogen atom. Plot the corresponding radial probability distributions f(r) 2 and compare with the analytical results for (a) a = 0.05A (cf. Fig.2.3.6 ) and (b) a = 0.1A (cf. Fig.2.3.7 )....
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- Spring '10
- Transistor, Fundamental physics concepts, discrete lattice, HKN lounge Problems, radial Schrodinger equation, corresponding radial probability