Chapt. 39 Photons and Matter Waves 293 for the stationary states ψ . b) For V = 0 (i.e., the free particle system), verify that ψ = e ikx are the unnormalized stationary states, where k = ± r 2 mE h − 2 . Why can’t these states be normalized? c) The in±nite square well has V = b0 , for 0 ≤ x ≤ a ; ∞ , for x < 0 and x > a . Verify that ψ = R 2 a sin( kx ) are the normalized solutions with boundary conditions ψ (0) = ψ ( a ) = 0. Also show that k = nπ a and E = h − 2 2 m p π a P 2 n 2 . 039 qfull 02000 3 5 0 tough thinking: complete set of states Extra keywords: A good challenge question. 5. It has been mathematically shown that the set of stationary state wave functions for a system constitute a COMPLETE SET : i.e., any function that obeys the same boundary conditions as the stationary state wave functions can be expanded as a linear combination of those stationary
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