5-HW Solutions

5-HW Solutions - HW #5 Schrdinger Equation Problem 1...

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HW #5 – Schrödinger Equation Phys320 –Spring 2007 (Reshchikov) p. 1 0 1 nm Ψ n = 4 0 Problem 1 (a) Draw the wave function of an electron confined to a 1-nm wide infinite well for the n = 4 state. (b) Find the wavelength λ, momentum p (and pc ), and energy E for the electron in this state (all in Modern Units). Alternatively: 22 2 2 6 2 26 ( ) (1240) 16 6.02 8 8 8 (0.511 10 )(1) 2 2(0.511 10 )6.02 6200 1240 0.2 6200 Kn K hh c EE n n e V mL mc L pc mc E eV c nm pp c λ == = = = ×× = =×= = = Problem 2 (a) Draw the wave function of an electron confined to a 0.5-nm wide finite well for the n = 5 state. (b) Find the wavelength λ (nm) , momentum in terms of pc (eV), and energy E for the electron in this state. Briefly describe how ψ (x) would change if the “walls” of the well were decreased in height. () 2 6 5 20 .5nm 2 0.2 nm 55 1240 eV nm 6200 eV 0.2 nm 6200 eV 37.6 eV .511 10 eV n L pc E = = × If the walls of the square well potential were decreased in height, then ψ (x) would decay slower in the regions outside the well. Number of peaks does not change. Amplitude slightly decreases due to “leakage” of some portion of wave function inside the walls.
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5-HW Solutions - HW #5 Schrdinger Equation Problem 1...

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